Q. 27

# The magnetic field existing in a region is given by

A square loop edge ℓ and carrying a current i, is placed with its edges parallel to the x-y axes. Find the magnitude of the net magnetic force experienced by the loop.

Answer :

Given-

A square loop with-

Magnetic field,

Length of the edge of a square loop = *l*

Electric current flowing through it = *i*

Given in the question that the loop is lies with its edges parallel to the *X*−*Y* axes.

In the fig, arrow shows the direction of force on different sides of the square.

Magnetic force acting due to presence of current on a small length l given by –

where,

= magnetic field

I = current

= length of the wire

Now,

Force on side AB -

Consider a differential element of length dx at a distance x from the origin along line AB

Force on this small element,

Force on the full length of AB,

Force on AB will be acting downwards.

Similarly, force on CD,

The net force acting vertically will be -

Force on AD,

Force on BC

Then, the net horizontal force

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A rectangular coil of 100 turns has length 5 cm and width 4 cm. It is placed with its plane parallel to a uniform magnetic field and a current of 2A is sent through the coil. Find the magnitude of the magnetic field B, if the torque acting on the coil is 0.2 N m^{–1}.

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