Question

A circular loop of radius 4 cm and carrying current 0.2 a is placed in a uniform magnetic field of induction 0.4 and perpendicular to the plane of the loop calculate the force on the arc of the circle of length 4pi/3

Answer 1

Force on a curved current carrying loop is given by formula

$F = \vec i (L X B)$

here

L = length vector which is a straight line joining the two free ends of the wire

B = magnetic field

now it is given that length of the arc of the wire is

$L = \frac{4\pi}{3}$

radius is given as R = 4 cm

now the angle subtended at the center will be given as

$\theta = \frac{L}{R} = \frac{\pi}{3}$

now the length vector which will join the two ends of the wire is given by

[/tex]L_{vector} = 2Rsin30 = R  = 4cm[/tex]

now by the above formula we will have

$L_{vector} = 4cm$

$i = 0.2 A$

$B = 0.4 T$

now the force on the wire is given by

$F = iLB = 0.2 * 0.04* 0.4$

$F = 3.2 * 10^{-3} N$

so the force on the arc given is 0.0032 N