# (a) Derive the expression for the torque acting on a current-carrying loop placed in a magnetic field. (b) Explain the significance of a radial magnetic field when a current-carrying coil is kept in it.

Let us consider a loop ABCD in a uniform magnetic field of strength B. and Let the current through the loop be I.

Consider force $F_{1}$ on arm AB and force $F_{2}$ on arm CD.

$F_{1}=F_{2}=IbB$

The net torque is given by -

$\tau = I\: \frac{a}{2}\: b\: B\: +I\: \frac{a}{2}\: b\: B\:$

$\tau = IAB$

Where A is the area of the loop

Now,

The magnetic moment of the loop.

$\vec{m}=I\vec{A}$

Therefore

$\tau = mB$

This is the expression for the torque acting on a current-carrying loop placed in a magnetic field.

(b) In a radial magnetic field, two sides of the rectangular coil remain perpendicular and other two ides remain parallel to magnetic field lines in all position of the coil.

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