Question

Assertion $A$ and $B$ are two conducting spheres of same radius. $A$ being solid and $B$ hollow. Both are charged to the same potential. Then, charge on $A=$ charge on $B$.
Reason Potentials on both are same.

• A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
• B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.
• C. If Assertion is true but Reason is false.
• D. If both Assertion and Reason are false.

Answer 1

Answer: (A)

Let $Q_A$ and $Q_B$ be the charges on the solid and the hollow conducting spheres respectively and $R$ be the radius of each sphere. When charge is given to a solid conducting sphere, it appears on the outer surface. For the calculation of electric field or potential due to a sphere (whether hollow or solid) at a point on or outside the sphere, the charge behaves as if it is concentrated at the centre of the sphere.
If $V_A$ and $V_B$ are potentials of two spheres, then
$V_A=\frac{1}{4\pi {\epsilon }_0}\frac{Q_A}{R}$
or $V_B=\frac{1}{4\pi {\epsilon }_0}\frac{Q_B}{R}$
Since, $V_A=V_B$
$\Rightarrow Q_A=Q_B$