A wire of length 44 cm carrying a current of 2 A is bent and the two ends are joined. This shape is placed in a uniform magnetic field of 50 mT. If the magnetic field in North-South direction, then the maximum torque acting on the shape is

Options

A. `1.54 times 10^(-3)Nm`
B. `0.77 times 10^(-3)Nm`
C. `3.08 times 10^(-3)Nm`
D. Zero

Answer

A

Explanation

Given, length of the wire, L = 44 cm
current flowing through the wire, I = 2A
and uniform magnetic field,
B =50 mT `=50 times 10^(-3)T`
Now, the area of the loop will be maximum when it is made in the form of a circle.
`therefore` Circumference of circle `=2pir`
`because` Circumference of circle = length of the wire (L)
or `" "2pir=44`
`" "r=44/(2pi)=7 cm`
`therefore` Area of loop, `A=pir^(2)`
`" "A=pi times 49 times 10^(-4)cm^(2)`
Now, the maximum torque acting on the shape,
`" "tau_("max")=BiA`
`" "=50 times 10^(-3) times 2 times 49pi times 10^(-4)`
`" "tau_("max")=1.54 times 10^(-3)Nm`