A spherical conducting shell of radius R has a charge q. A point charge Q is placed at its centre. The electrostatic potential at a point P, distant ( R /2) from the centre of the shell is :-

Question

A spherical conducting shell of radius R has a charge q. A point charge Q is placed at its centre. The electrostatic potential at a point P, distant ( R /2) from the centre of the shell is :- (A) (( q + Q )/4 π ε0) (2/ R ) (B) (2 Q /4 π ε0 R ) (C) (2 Q/4 π ε0 R )-(2 q /4 π ε0 R ) (D) (2 Q/4 π ε0 R )+( q /4 π ε0 R )

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/b64a2c503dacd4de3b4b6c155086ca83-.png" /> V p = Potential due to Q + Potential due to sphere V p =( kQ / R / 2)+( kq / R ) ⇒ V p =( k / R )(2 Q + q )

Q. A spherical conducting shell of radius $R$ has a charge q. A point charge $Q$ is placed at its centre. The electrostatic potential at a point P, distant $\frac{R}{2}$ from the centre of the shell is :-

$\frac{( q + Q )}{4 π ε _{0}} \frac{2}{R}$

$\frac{2 Q}{4 π ε _{0} R}$

$\frac{2 Q}{4 π ε _{0} R} - \frac{2 q}{4 π ε _{0} R}$

$\frac{2 Q}{4 π ε _{0} R} + \frac{q}{4 π ε _{0} R}$

$V_{p} =$ Potential due to $Q +$ Potential due to sphere
$V_{p} = \frac{k Q}{R /2} + \frac{k q}{R}$
$\Rightarrow V_{p} = \frac{k}{R} (2 Q + q)$

Q. A spherical conducting shell of radius R has a charge q. A point charge Q is placed at its centre. The electrostatic potential at a point P, distant 2R​ from the centre of the shell is :-

4πε0​(q+Q)​R2​

4πε0​R2Q​

4πε0​R2Q​−4πε0​R2q​

4πε0​R2Q​+4πε0​Rq​