Current Electricity — JEE Advanced · 2016 · 22 May 2016 · Paper 2 Question with Solution

Passage

Consider an evacuated cylindrical chamber of height

h

having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius

r ≪ h

. Now a high voltage source (HV) is connected across the conducting plates such that the bottom plate is at

+ V_{0}

and the top plate at

- V_{0}

. Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)

PARAGRAPH 2

Consider an evacuated cylindrical chamber of height

h

r ≪ h

. Now a high voltage source (HV) is connected across the conducting plates such that the bottom plate is at

+ V_{0}

and the top plate at

- V_{0}

(A)zero
(B)proportional to the potential $V_{0}$
(C)proportional to $V_{0}^{1/2}$
(D)proportional to $V_{0}^{2}$ ✓ Correct

Answer: (D)

Solution

The charge on each ball is proportional to the capacitance and voltage:

Q \propto V_{0}

The electric field

E = \frac{2 V _{0}}{h}

, so acceleration

a = \frac{QE}{m} = \frac{Q \cdot 2 V _{0}}{mh} \propto V_{0}^{2}

Time for one trip:

h = \frac{1}{2} a t^{2}

, giving

t \propto \frac{1}{a} \propto \frac{1}{V _{0}}

Average current:

I_{a v} = \frac{Q}{t} \propto \frac{V _{0}}{1/ V _{0}} = V_{0}^{2}

JEE Advanced · 2016 · 22 May 2016 · Paper 2 · Single correct option

JEE Advanced · 2016 · 22 May 2016 · Paper 2 · Current Electricity

Solution

More JEE Advanced questions on Current Electricity