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
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.