Question

Q2) At distance d from a point charge of magnitude q the potential is V.
Which of the following is the potential at a distance 4d from a point charge of magnitude 2q?
a) V/4
b) V/2
c) V
d) 2V

Answer 1

Answer:

$V/2$.

Explanation:

The electric potential $E$ at a distance of $d$ from a point charge can be modelled with the following formula:

$\displaystyle E = \frac{k\, q}{d}$,

Where:

• $k$ is Coulomb's Constant,
• $q$ is the electrostatic charge on that point charge, and
• $d$ is the distance from the point charge.

Note that electric potential is proportional to the charge, and inversely proportional to the distance from the charge. If the original potential in this question is $(k\, q) / d$, the new electric potential would be:

$\displaystyle \frac{k\, (2\, q)}{(4\, d)} = \frac{1}{2}\, \left(\frac{k\, q}{d}\right)$.

In other words, the new electric potential would be one-half the initial value.