Question

Two points $A$ and $B$ are located in diametrically opposite directions of a point charge of $+ 2\mu C$ at distance $2m$ and $1m$ respectively from it. The potential difference between $A$ and $B$ is:
(A) $3 \times {10^3}V$
(B) $6 \times {10^4}V$
(C) $- 9 \times {10^3}V$
(D) $- 3 \times {10^3}V$

Answer 1

To find out the potential difference between$A$and$B$, we need to find out electric potential at point $A$ and $B$ from point charge, then subtract electric potential at point $B$from electric potential at point$A$.
Given:
Point charge,$q = + 2\mu C = + 2 \times {10^{ - 6}}C$
Distance of point $A$ from point charge, ${r_{_A}} = 2m$
Distance of point $B$ from point charge, ${r_{_B}} = 1m$

Complete step by step solution:
To find out the electric potential difference between$A$and$B$, we use formulas to find electric potential.
Electric potential at point $A$from point charge.
Electric Potential, ${V_A} = \dfrac{q}{{4\pi {\varepsilon _0}{r_A}}}$
We will put the values of $q$and ${r_A}$in above formula
$\Rightarrow {V_A} = \dfrac{{ + 2 \times {{10}^{ - 6}}}}{{4\pi {\varepsilon _0}2}}$
We know that, $\dfrac{1}{{4\pi {\varepsilon _0}}} = k$ and $k$ is a Coulomb's law constant.
The value of Coulomb's constant depends on the medium of the charged objects. As per the question medium of charge object is air. So we will take value of coulomb’s constant is approximately $9 \times {10^9}N{m^2}/{C^2}$
${V_A} = \dfrac{{9 \times {{10}^9} \times 2 \times {{10}^{ - 6}}}}{2} = 9 \times {10^3}V$
We will find out electric potential at point $B$from point charge
$\Rightarrow {V_B} = \dfrac{{ + 2 \times {{10}^{ - 6}}}}{{4\pi {\varepsilon _0}1}}$(Put$\dfrac{1}{{4\pi {\varepsilon _0}}} = k = 9 \times {10^9}N{m^2}/{C^2}$)
${V_B} = 9 \times {10^9} \times 2 \times {10^{ - 6}} = 18 \times {10^3}V$
Now, we will find electric potential difference
$\Delta V = {V_A} - {V_B}$
Put values of ${V_A}$and ${V_B}$in above equation
$\Delta V = 9 \times {10^3} - 18 \times {10^3} = - 9 \times {10^3}V$

Hence, option c is the correct option.

Note: Point to be noted that we should remember the value of Coulomb's law constant, because if we put the individual values of $\pi$and ${\varepsilon _0}$ then try to calculate, then this question’s calculation might be complex.