Test: Torque on Current Carrying Loop - JEE MCQ

A device which converts electrical energy into mechanical energy is called an electrical motor.
The working principle of an electric motor depends on the magnetic and electric field interaction.
There are two types of electric motor and they are:
AC motor: Converts alternating current into mechanical power. Linear motor, synchronous motor, and induction motor are the three types of AC motor.
DC motor: Converts direct current into mechanical power. Self-excited motor and separately excited are the two classifications of DC motor.
 

A current (i) in a magnetic field ( B) experiences a force ( F) given by the equation

 F = i (l × B) 

or F = ilB sin θ,

where l is the length of the wire, represented by a vector pointing in the direction of the current.

a², = I A B
The 40cm of wire can bent into a square with slides of 10cm
A=(10cm)²=100 cm²
τ=I A B
τ=(20A)(100cm²)(0.52T)
τ=1040 A cm²T[1m²/10⁴ cm²]
τ=0.1040 N-m

 Answer :- c

Solution :- When a charged particle moves in a magnetic field, a force is exerted on the moving charged particle. The formula for the force depends on the charge of the particle, and the cross product of the particle's velocity and the magnetic field.

The magnetic moment of this loop is in direction perpendicular to the plane of loop and coming out of the plane. The magnetic field is also directed perpendicularly into the loop. So, magnetic moment magnetic field are antiparallel. The torque acting on the loop, which is given by the cross product of moment and field, is zero since sin 180 = 0

The torque on a current loop depends upon the area of the current loop, when the magnetic field is perpendicular to the plane of the loops the torque has its maximum value,
Τ=I A B
We know I and B for all these cases but A depends upon the geometry. The circle has the greatest area so it should provide the greatest torque.

A=0.01m², I=100A, B=0.1T, θ=90^o,sinθ=1
Now magnetic moment M =I×A
Torque, τ=M×B
                =MBsinθ
                =IAB
                =100×0.01×0.1=0.1Nm.

Correct answer is A.

As the magnetic field is parallel to the charge, no magnetic Lorentz force will act on it and it will move undeviated with constant velocity.