(a) Derivation of expression for torque
(b) Significance of radial magnetic field.
Consider the simple case when a rectangular loop is placed in a uniform magnetic field B that is in the plane of the loop.
Force on arm AB=F1=IbB (directed into the plane of the loop)
Force on arm CD=F2=IbB (directed into the plane of the loop)

Therefore the magnitude of the torque on the loop due to these pair of forces
τ=‌F1‌

a

2

+F2‌

a

2

=‌I(ab)B
=‌IAB=mB
‌(A=ab=‌ area of the loop ‌)
Alternatively,
Also accept if the student does calculations for the general case and obtains the result.
‌ Torque ‌=IABsin‌ϕ
Alternatively,
Also accept if the student says that the equivalent magnetic moment (m), associated with a current carrying loop is

→

m

=LA

^

n

‌ ( ‌A=‌ Area of loop) ‌
The torque, on a magnetic dipole, in a magnetic field, is given by

→

τ

‌=

→

m

×

→

B

∴‌τ=IA(

^

n

×

→

B

)
Hence
Magnitude of torque is =IABsin‌ϕ
(b) When a current carrying coil is kept a radial magnetic field the corresponding moving coil galvanometer would have a linear scale.
Alternatively,
"In a radial magnetic field two sides of the rectangular coil remain parallel to the magnetic field lines while its other two sides remain perpendicular to the magnetic field lines. This holds for all positions of the coil".