Electrostatics Test - 13

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.

Aluminium electrolytic capacitors have the Aluminium foil anode (positive terminal) which is attached and covered with a layer of Aluminium Oxide which acts as a dielectric. The whole assembly is covered using a paper separator soaked in electrolyte such as, Borax or Glycol and covered by Aluminium foil which acts as cathode ( negative electrode)

A positive charge experiences a force in the direction of the field.
If it moves opposite to the direction of the field, negative work is done by the electric field on the charge.
Potential energy of the charge increases since an external source is required to do work on the charge against the direction of the field, and the work done is stored in the charge as its potential energy.

A submarine cable consists of an inner conductor which carries power. This conductor is covered by an insulator, which acts as a dielectric. The dielectric material is covered by a metal coating called shield, which is connected to ground. 
The cable acts as a cylindrical capacitor, with the conductor acting as the inner cylinder, and the metal shield as the outer cylinder which is connected to earth.

Let the two conductors have capacitances C₁ and C₂ and let their potentials be V₁ and V₂ .
Total initial energy of the conductors,  U_i = (1/2)C₁V₁₂ + (1/2)C₂V₂₂
When two charged conductors are connected by a wire, the flow of charge stops when the potentials are equalized.
Let V be the common potential and Q₁ and Q₂ be the charges on the conductors after the common potential is attained.

The final energy

Therefore,

The electric field inside a cavity is always zero. The potential inside a cavity of a conductor is constant.
The potential difference between any two points inside a charged conductor is zero. This phenomenon is called electrostatic shielding.

Q_total​ = 4×10⁻²C

Charge distribution α capacitance α radius  

Q_small​:Q_big​=1:3

Q_big​= 3/4 ×4×10⁻² = 3×10⁻²C

Since there is an equal number of positive and negative charges on capacitor A, the charges won't flow to capacitor B as the charge are held by strong electrostatic force.
The capacitor B will acquire a charge only if a battery (driving force) is put in the circuit.

If P is at positive potential, then Q is at negative potential and R is at positive potential. The system therefore reduces to 3 capacitors in parallel. C= 9μF

When two capacitors C1 and C2 are connected in series, the reciprocal of the equivalent capacitance in series is equal to the sum of the reciprocals of the two individual capacitances.

It has value lesser than the least value of capacitance.

When an uncharged capacitor is connected to a battery, charges flow from the poles of the battery to the plates of the capacitor and this process continues till the potential across the capacitor attains the potential difference of the battery. The current flow in the circuit till the time the capacitor is charged and then it ceases.