Test: Electrostatic Potential & Capacitance(5 Nov) - JEE MCQ

The potential difference between any two points inside the hollow conductor is zero. This means that the potential at all points inside the hollow charged conductor is the same and it is equal to the value of the potential at its surface.

The electric field on the surface of a hollow conductor is maximum and it drops to zero abruptly inside the conductor.

E = - dV/dr

When the potential at all points on the surface is the same, such a surface is called an equipotential surface.

The potential difference between any two points on an equipotential surface is zero.

An electroscope is a device that measures the potential difference.
If it is connected in parallel to the capacitor, the potential across it will be equal to the potential across the capacitor, which is equal to the potential across the battery.
On decreasing the battery potential, the potential difference across the electroscope reduces, and hence the reading reduces. 

The intial energy stored in the capacitor C of potential difference V is
E = (1/2) CV² 
When the p.d increased by ΔV, the energy stored will be ΔE.

The capacitance of a spherical conductor of radius R is 

When a charged particle moves in an electric field, its electric potential energy decreases, its kinetic energy will increase i.e. the total energy is conserved.

The initial energy of the capacitor of capacitance C and charge Q₁,  

When the charge increases to Q₂ the change in the energy of the capacitor, 

Given percentage increase of energy,

Since, Q₂ - Q₁ = 2
⇒ Q₁ = 20 C

When capacitors are connected in series, they have equal charge but the potential difference across them is given by

Energy stored in the capacitor
This is released as heat when the capacitor discharges through the metal block. The quantity of heat = mass xs p.heatx rise in temperature. 
Q = m x s x Δθ = 0.1 x 2.5 x 10² x 0.4 = 10 J
U = Q; 2 x 10⁴ C = 10; C = 5 x 10^-4 F = 500 μF

Capacitance of the small drop of radius r C₈ = 4πε₀r  and that of the big drop of radius R is C_B = 4πε₀R .  
The volume of 64 small drops, 
The ratio 

The breakdown of the potential of the capacitor is 220 V.

In order to prevent damage to a capacitor, it should be always used in a circuit where the p.d is less than its breakdown potential. The p.d difference can only be 200 V.

When a dielectric of constant K is introduced between the plates of a capacitor, the potential V reduces to V/K. Therefore K=8

When a dielectric is introduced between two charged plates of a capacitor having a charge Q and maintained at a potential difference of V, a reverse electric field is set up inside the dielectric due to dielectric polarization. This reduces the electric field in between the plates. The potential is also reduced.

Maximum potential is dependent on the charge on the plates. As the charge remains constant, the presence of the dielectric decreases the maximum potential between the plates.

Electric field lines show the direction of the electric field at the point. If the electric field lines were tangential, parallel, or opposite to the equipotential surface, a tangential field will exist on the surface and work done in moving a charge on the surface is not zero.

Therefore electric field lines are always perpendicular to the equipotential surface.