Select the correct answer.

A charge of [tex]$6.7 \times 10^{-15}$[/tex] coulombs is located at a point where its potential energy is [tex]$5.6 \times 10^{-12}$[/tex] joules. What is the electric potential at that point?

A. [tex][tex]$2.3 \times 10^2$[/tex][/tex] volts
B. [tex]$4.7 \times 10^2$[/tex] volts
C. [tex]$8.4 \times 10^2$[/tex] volts
D. [tex][tex]$9.2 \times 10^2$[/tex][/tex] volts



Answer :

To determine the electric potential at the point, we can use the formula that relates electric potential (V), potential energy (U), and charge (q):

[tex]\[ V = \frac{U}{q} \][/tex]

Given:
- Charge, [tex]\( q = 6.7 \times 10^{-15} \)[/tex] coulombs
- Potential energy, [tex]\( U = 5.6 \times 10^{-12} \)[/tex] joules

Plugging these values into the equation, we get:

[tex]\[ V = \frac{5.6 \times 10^{-12} \text{ joules}}{6.7 \times 10^{-15} \text{ coulombs}} \][/tex]

Simplifying the expression:

[tex]\[ V = \frac{5.6 \times 10^{-12}}{6.7 \times 10^{-15}} \][/tex]

This division results in:

[tex]\[ V \approx 835.8208955223881 \text{ volts} \][/tex]

Given the options:
A. [tex]\( 2.3 \times 10^2 \)[/tex] volts
B. [tex]\( 4.7 \times 10^2 \)[/tex] volts
C. [tex]\( 8.4 \times 10^2 \)[/tex] volts
D. [tex]\( 9.2 \times 10^2 \)[/tex] volts

The value [tex]\( 835.8208955223881 \)[/tex] volts corresponds approximately to option:
C. [tex]\( 8.4 \times 10^2 \)[/tex] volts

Therefore, the correct answer is:

C. [tex]\( 8.4 \times 10^2 \)[/tex] volts

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