find the change in electrical potential energy of an electron as it moves from a distance r1=1.0cm to r2=3.0cm from a point charge of 0.5uc

Question

Visualize a physics-based scenario demonstrating the fundamental concept of electric potential energy. Show an electron starting at a distance marked as 'r1' close to a positively charged particle. The electron then journeys away from the positive charge, signifying an increase in distance, marked as 'r2'. The charged particle in the center should glow with light representing positive charge (0.5uc). Please avoid including any text in the image.

find the change in electrical potential energy of an electron as it moves from a distance r1=1.0cm to r2=3.0cm from a point charge of 0.5uc

Answer 1

To find the change in electrical potential energy (ΔPE) of an electron moving from one distance to another from a point charge, we can use the formula:

ΔPE = q * ΔV

Where:
ΔPE is the change in electrical potential energy
q is the charge of the electron
ΔV is the change in electrical potential (also known as voltage)

To calculate ΔV, we can use the formula:

ΔV = k * q / r

Where:
k is the electrostatic constant (k ≈ 8.99 x 10^9 N m²/C²)
q is the charge of the point charge (given in micro-coulombs)
r is the distance between the electron and the point charge (given in meters)

Now, let's calculate the change in electrical potential energy (ΔPE) step by step:

Step 1: Convert the charge from micro-coulombs (uc) to coulombs (C):
Given q = 0.5 uc
1 C = 1 x 10^6 uc
So, q = 0.5 x 10^(-6) C

Step 2: Calculate ΔV:
Given r1 = 1.0 cm = 0.01 m (converted to meters)
Given r2 = 3.0 cm = 0.03 m (converted to meters)

ΔV = k * q * (1/r2 - 1/r1)
= (8.99 x 10^9 N m²/C²) * (0.5 x 10^(-6) C) * (1/0.03 - 1/0.01)

Step 3: Calculate ΔPE using ΔPE = q * ΔV:
ΔPE = (0.5 x 10^(-6) C) * ΔV

Calculate the subtraction of the fractions inside ΔV, then substitute the value of ΔV into the equation to get ΔPE, and simplify the expression to obtain the final result.