deflects and gradually comes to the original position

in a time, which is large compared to the time constant.

Explanation: The deflection in a compass needle are because of

magnetic field around the region of the compass. The magnetic field

arises due to charging of the capacitor which creates a varying

electric field. This varying electric field produces a changing electric

field through the capacitor plates. Due to this changing electric flux, a current called the displacement current arises in the capacitor. The

current I_d is related to the electric flux as

…. (i)

where ϕ_E is the time varying electric flux through the plane surface

and ϵ₀ is the electric permittivity of free space(vacuum) and is equal

to 8.85 × 10^-12 C² N^-1 m^-2.

According to Ampere-Maxwell’s law of electromagnetism, the total

magnetic field is due to current due to charge carriers and the

current due to time varying electric flux. Ampere-Maxwell law is the

extension of Ampere Circuital Law. The mathematical relation

is

…(ii)

where B is the magnetic field, dl is small element of length of an

Amperian loop, μ₀ is the magnetic permeability of free space and its value is 4π × 10^-7 T m A^-1, and I_enclosed is the current due to charge carriers.

From (i) and (ii)

…(iii)

According to Gauss’s Law of electrostatics, the electric flux through

a surface is equal to 1/ϵ₀ times the charge enclosed by it.

The charge enclosed by the capacitor plates is changing with time

as the capacitor is charging. The charge is given as

where

C=capacitance of the capacitor

V=potential of the battery

R=resistance of the resistor connected in series

Using the above two relations in (iii)

So the magnetic field depends on the charge of the capacitor. The

needle will show deflection till the capacitor gets charged to a

specific value at a time τ called the time constant. is the time

constant of the capacitor. Charging after this time will be gradual so

the needle will come to its original position.