Question

A compass needle is placed in the gap of a parallel plate capacitor. The capacitor is connected to a battery through a resistance. The compass needle

Options

• does not deflect

• deflects for a very short time and then comes back to the original position

• deflects and remains deflected as long as the battery is connected

• deflects and gradually comes to the original position in a time that is large compared to the time constant

Answer 1

deflects and gradually comes to the original position in a time that is large compared to the time constant

The compass needle deflects due to the presence of the magnetic field. Inside the capacitor, a magnetic field is produced when there is a changing electric field inside it. As the capacitor is connected across the battery, the charge on its plates at a certain time t is given by :

`Q = CV(1-e^(-"t/RC"))`,

where
Q =  charge developed on the plates of the capacitor
R =  resistance of the resistor connected in series with the capacitor 
​C =  capacitance of the capacitor
V =  potential difference of the battery
The time constant of the capacitor is given, τ = RC

The capacitor keeps on charging up to the time τ. The development of charge on the plates will be gradual after t = RC. The change in  electric field will be up to the time the charge is developing on the plates of the capacitor. Thus, the compass needle ​deflects and gradually comes to the original position in a time that is large compared to the time constant.