Python4Physics LAB
Classic v1
Home > Python > Introduction to Python

Ch. 1.5 For Loop

Chapters Index
Program 1

For Loop

Python 3.11 Ready 

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                    

                    

                

                                

                    
                    

                        

                            Program 2
                            
For Loop

                        

                        

                            
                            
                            
                        

                    


                    
                    

                        
                        

                            

                                 Python 3.11
                                Ready
                            

                            

                                
                                
                            

                            
                            

                                

                                    
                                    
                                    
                                    
                                

                                

                                    
                                

                            

                        


                        
                        

                            

                                
                                
                                                            


                            
                            

                                

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                    

                    

                

                                

                    
                    

                        

                            Program 3
                            
For Loop

                        

                        

                            
                            
                            
                        

                    


                    
                    

                        
                        

                            

                                 Python 3.11
                                Ready
                            

                            

                                
                                
                            

                            
                            

                                

                                    
                                    
                                    
                                    
                                

                                

                                    
                                

                            

                        


                        
                        

                            

                                
                                
                                                            


                            
                            

                                

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                    

                    

                

                                

                    
                    

                        

                            Program 4
                            
For Loop

                        

                        

                            
                            
                            
                        

                    


                    
                    

                        
                        

                            

                                 Python 3.11
                                Ready
                            

                            

                                
                                
                            

                            
                            

                                

                                    
                                    
                                    
                                    
                                

                                

                                    
                                

                            

                        


                        
                        

                            

                                
                                
                                                                
                                                            


                            
                            

                                

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                        

                                

                                                                        

                                        
 Mathematical Problem Formulation

                                        
Understanding Python's range() Function



range(6): Generates a sequence of integers from 0 to 5 (inclusive of 0 but exclusive of 6).



Iteration with for Loop:


for number in range(6): Iterates over each integer in the sequence.



Print the Current Integer:


print(number): Prints the current integer on each iteration.

                                    

                                    
                                                                    

                            

                                                    

                    

                

                                

                    
                    

                        

                            Program 5
                            
For Loop

                        

                        

                            
                            
                            
                        

                    


                    
                    

                        
                        

                            

                                 Python 3.11
                                Ready
                            

                            

                                
                                
                            

                            
                            

                                

                                    
                                    
                                    
                                    
                                

                                

                                    
                                

                            

                        


                        
                        

                            

                                
                                
                                                                
                                                            


                            
                            

                                

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                        

                                

                                                                        

                                        
 Mathematical Problem Formulation

                                        
range(1, 10, 2): Generates a sequence of integers starting from 1 up to (but not including) 10, with a step of 2. This means it will include every second number starting from 1 to 9. 



for number in range(1, 10, 2): Iterates over each integer in the sequence produced by range(1, 10, 2).

                                    

                                    
                                                                    

                            

                                                    

                    

                

                                

                    
                    

                        

                            Program 6
                            
For Loop

                        

                        

                            
                            
                            
                        

                    


                    
                    

                        
                        

                            

                                 Python 3.11
                                Ready
                            

                            

                                
                                
                            

                            
                            

                                

                                    
                                    
                                    
                                    
                                

                                

                                    
                                

                            

                        


                        
                        

                            

                                
                                
                                                            


                            
                            

                                

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                    

                    

                

                                

                    
                    

                        

                            Program 7
                            
For Loop

                        

                        

                            
                            
                            
                        

                    


                    
                    

                        
                        

                            

                                 Python 3.11
                                Ready
                            

                            

                                
                                
                            

                            
                            

                                

                                    
                                    
                                    
                                    
                                

                                

                                    
                                

                            

                        


                        
                        

                            

                                
                                
                                                            


                            
                            

                                

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                    

                    

                

                                

                    
                    

                        

                            Program 8
                            
For Loop

                        

                        

                            
                            
                            
                        

                    


                    
                    

                        
                        

                            

                                 Python 3.11
                                Ready
                            

                            

                                
                                
                            

                            
                            

                                

                                    
                                    
                                    
                                    
                                

                                

                                    
                                

                            

                        


                        
                        

                            

                                
                                
                                                            


                            
                            

                                

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                    

                    

                

                                

                    
                    

                        

                            Program 9
                            
For Loop

                        

                        

                            
                            
                            
                        

                    


                    
                    

                        
                        

                            

                                 Python 3.11
                                Ready
                            

                            

                                
                                
                            

                            
                            

                                

                                    
                                    
                                    
                                    
                                

                                

                                    
                                

                            

                        


                        
                        

                            

                                
                                
                                                                
                                                            


                            
                            

                                

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                        

                                

                                                                        

                                        
 Mathematical Problem Formulation

                                        

        
   


Outer Loop (for i in range(1, 4)):


The outer loop goes through numbers \(1\), \(2\), and \(3\). 
range(1, 4) means "start at \(1\) and go up to (but not including) \(4\)." So, it will produce the numbers \(1\), \(2\), and \(3\).



Inner Loop (for j in range(10, 13)):


For each value of \(i\) from the outer loop, this inner loop goes through numbers \(10\), \(11\), and \(12\). 
range(10, 13) means "start at \(10\) and go up to (but not including) \(13\)." So, it produces the numbers \(10\), \(11\), and \(12\).


Output of Nested Loops



First Group: When i = 1:


It prints 1 with 10, 11, and 12.



Second Group: When i = 2:


It prints 2 with 10, 11, and 12.



Third Group: When i = 3:


It prints 3 with 10, 11, and 12.

                                    

                                    
                                                                    

                            

                                                    

                    

                

                                

                    
                    

                        

                            Program 10
                            
For Loop

                        

                        

                            
                            
                            
                        

                    


                    
                    

                        
                        

                            

                                 Python 3.11
                                Ready
                            

                            

                                
                                
                            

                            
                            

                                

                                    
                                    
                                    
                                    
                                

                                

                                    
                                

                            

                        


                        
                        

                            

                                
                                
                                                            


                            
                            

                                

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                    

                    

                

                                

                    
                    

                        

                            Program 11
                            
For Loop

                        

                        

                            
                            
                            
                        

                    


                    
                    

                        
                        

                            

                                 Python 3.11
                                Ready
                            

                            

                                
                                
                            

                            
                            

                                

                                    
                                    
                                    
                                    
                                

                                

                                    
                                

                            

                        


                        
                        

                            

                                
                                
                                                            


                            
                            

                                

                                

                            


                            
                            

                                

                                    
Click "Run Code" to execute script and render figures.

                                

                            


                            
                                                    

                    

                

                            
            
            
            
            
            

                

                    

                         Theoretical Principles & Computational Physics Guide
                    

                    

                        For Loop: Deterministic Iteration & Finite Series Summations                    

                    

                         Dr. Alorika Chatterjee & Dr. Anirban Shaw
                         Science & Physics Learners
                         Python 3 / NumPy / SciPy
                    

                


                
                

                    

                         1. Core Principles & Theoretical Framework
                    

                    

                        
                    

                        
 Deterministic Loops: Iterates over a known number of discrete time steps, spatial grid nodes, or particle indices.

                        
 Series Evaluation: Computes finite expansions such as multipole potentials, Fourier series, and Taylor polynomials.

                        
 Time Stepping: Advances dynamical systems sequentially: $t_n = t_0 + n \Delta t$.

                    
                    

                


                
                

                    

                         2. Mathematical Formulation & Algorithmic Pipeline
                    

                    

                        
                    
Total electric potential from a discrete array of $N$ point charges:

                    
$$ \Phi(\mathbf{r}) = \sum_{i=1}^N \frac{q_i}{4\pi\varepsilon_0 |\mathbf{r} - \mathbf{r}_i|} $$
                    

                


                
                

                    

                         3. Numerical Mechanics & Implementation Logic
                    

                    

                        
                    
    
                        
  • Accumulator Pattern: Initialize total sum (e.g. total_potential = 0.0) before the loop.
    • 
                        
  • Range Iterator: Use range(start, stop, step) to index through discrete integer steps without memory overhead.
    • 
                        
  • State Storage: Record time-series coordinates in accumulator lists at each step for post-processing.
    • 
                    
                    

                


                
                

                    

                         4. Relevant Computational Practice Exercises
                    

                    

                                                    

                                Exercise 1
                                

                                    Compute the total gravitational field of $N = 50$ equal masses placed uniformly along the circumference of a circle.                                

                                
                            

                                                    

                                Exercise 2
                                

                                    Evaluate the Taylor series expansion for $\cos(x)$ up to $N = 10$ terms and compare accuracy against <code>math.cos(x)</code>.                                

                                
                            

                                                    

                                Exercise 3
                                

                                    Integrate a uniform velocity trajectory $x(t)$ over 200 discrete time steps of $\Delta t = 0.01\text{ s}$.                                

                                
                            

                                            

                


                
                

                     Standard Literature & References:
                    
    
                                                    
  • Mark Newman, "Computational Physics", University of Michigan (2013).
    •