Question

what is the electric potential energy of a charge that experiences a force of 3.6 × 10⁻⁴ n when it is 9.8 × 10⁻⁶ m from the source of the electric field?
○ 3.5 × 10⁻⁸ j
○ 4.6 × 10⁻⁴ j
○ 2.7 × 10⁻¹ j
○ 3.7 × 10⁰ j

Explanation:

Step1: Recall the formula for electric potential energy (U) in terms of force (F) and distance (d). The formula is \( U = F \times d \) (assuming the force is conservative and we're calculating the work done against the force, which equals the potential energy change in this context).

Given \( F = 3.6 \times 10^{-4} \, \text{N} \) and \( d = 9.8 \times 10^{-5} \, \text{m} \).

Step2: Substitute the values into the formula.

\( U=(3.6\times 10^{-4})\times(9.8\times 10^{-5}) \)
First, multiply the coefficients: \( 3.6\times9.8 = 35.28 \)
Then, multiply the powers of 10: \( 10^{-4}\times10^{-5}=10^{-4 + (-5)} = 10^{-9} \)
So, \( U = 35.28\times 10^{-9} \, \text{J} \)
Convert to scientific notation: \( 35.28\times 10^{-9}=3.528\times 10^{-8} \, \text{J}\approx3.5\times 10^{-8} \, \text{J} \)

Answer:

\( 3.5\times 10^{-8} \, \text{J} \) (corresponding to the first option)