Question

The nature of the magnetic field in a moving galvanometer is a Radial magnetic field. State True or False.

Answer 1

Hint: In a galvanometer the torque on the current carrying coil is balanced by the torque of torsion wire. By equating the two torques, we can calculate the relation between current and angle of twist. But for that relation to be linear radical magnetic fields are must.

Complete Step By Step Solution:
Galvanometer is a device which is used to measure electric current in a circuit. It consists of a moving coil suspended by a torsion wire, placed in a radial magnetic field.
When current is passed through this coil, it experiences a magnetic force, which produces a torque in the coil. The torque acting on a coil of magnetic moment M placed in the magnetic field B is given by
Torque =$M\times B$,
Where M is magnetic moment and is defined as
Magnetic moment =$i\overset{\to }{\mathop{A}}\,$,
where $i$ is the current passing through the coil and $\overset{\to }{\mathop{A}}\,$ is the area vector of the coil.
So, the torque is
Torque =$i\overset{\to }{\mathop{A}}\,\times \overset{\to }{\mathop{B}}\,=iAB\sin \alpha $,
where $\alpha $is the angle between magnetic field B and area vector of coil.
This torque is balanced by the torque due to torsion wire given by
Torque due to wire =$c\theta $,
So we can say
$c\theta =iAB\sin \alpha $
$i=\dfrac{c\theta }{AB\sin \alpha }$
The advantage of using radical magnetic fields is that in such a field angle between magnetic field and area vector is always ${{90}^{\circ }}$. So, current through the coil becomes directly proportional to the twist in the wire. We can measure twist of wire and thereby calculate current through the coil, which will be the same as current through the circuit.
$i=\dfrac{c\theta }{AB}$.
Hence, the statement “nature of the magnetic field in a moving galvanometer is a Radial magnetic field” is true.

Note: A more sensitive galvanometer is the one which shows more deflection (more twist of wire) for the same current. To increase the sensitivity of the galvanometer we can increase the area of the coil, increase the strength of the magnetic field and decrease the torsion constant of the wire.