Question

A soap bubble is given a negative charge, then its radius.
(A) decrease
(B) increase
(C) remains unchanged
(D) none of these

Answer 1

Hint The radius of the soap bubble can be determined by using the electric potential produced by the point charge $Q$, by using this formula and the conditions which are given in the question, the radius of the soap bubble can be determined.
Useful formula:
The electric potential produced by the point charge can be determined by,
$V = \dfrac{{kQ}}{R}$
Where, $V$ is the potential developed in the soap bubble, $k$ is the constant, $Q$ is the point charge which is placed in the centre of the bubble and $R$ is the radius of the soap bubble.

Complete step by step solution
Given that,
The soap bubble is given as negative charge.
By the formula,
The electric potential produced by the point charge can be determined by,
$V = \dfrac{{kQ}}{R}\,.......................\left( 1 \right)$
Where, $V$ is the potential developed in the soap bubble, $k$ is the constant, $Q$ is the point charge which is placed in the centre of the bubble and $R$ is the radius of the soap bubble.
In the above equation (1), the charge and the radius both are inversely proportional. If the charge is given as negative means, the charge is decreasing, so that the potential difference also decreases, if the potential difference decreases, then the radius is increased.

Hence, the option (B) is the correct answer.

Note The potential developed is directly proportional to the charge which is placed in the centre of the circle and the potential developed is inversely proportional to the radius of the circle. As the charge increases, the potential developed also increases. As the charge decreases, the potential developed also decreases, if the potential developed decreases then the radius is increased.