A rigid wire consists of a semicircular portion of radius R and two straight sections figure. The wire is partially immersed in a perpendicular magnetic field B as shown in the figure. Find the magnetic force on the wire if it carries a current i.

Given-

Radius of the semi-circular portion = R

Perpendicular Magnetic field = B

Electric current flowing through the wire = I A

Given in the question, the wire is partially immersed in a perpendicular magnetic field.

As AB and CD are straight wires of length l each and strength of the magnetic field is also same on both the wires, the force acting on these wires will be equal in magnitude

Direction of force can be found out using Fleming’s left hand rule.

So, their directions will be opposite to each other.

So, the magnetic force on the wire AB and the force on the wire CD are equal and opposite to each other. Both the forces cancel out each other.

Therefore, only the semicircular loop RC will experience a net magnetic force.

Here, angle between the length of the wire and magnetic field, θ = 900

We know ,magnetic force acting
on a current carrying wire in an uniform magnetic field is given by

where,

B= magnetic field

I = current

l = length of the wire

and θ = the angle between B and l

Here, length l = 2R

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