Question

A semicircular wire PQS of radius R is connected to a wire bent in the form of a sine curve to form a closed loop as shown in the figure. If the loop carries a current i and is placed in a uniform magnetic field B, then
the total force acting on the sine curve is​

Answer 1

Hi there,

Since the diagram for this question was not provided so I looked for it on the internet and found a figure (attached below) which satisfies with the question completely. Hope the figure attached below is the correct one.

Answer:

The total force acting on the sine curve is zero.

Explanation:

Given data:

As shown in the figure below, PQS is a semi-circular closed loop wire of radius “R”, which is bent in the form of a sine curve.

Current in the loop is “i”

Loop is placed in a uniform magnetic field “B”

To find: total force acting on the sine curve

We know that force acting on a wire loop carrying current and placed in a uniform magnetic field is given by

F = B * i * (displacement of the current) = B * i * 2R

Now, let's divide the sinusoidal loop into two parts to understand the net force acting on it. From the figure, let the first half be the hemisphere and the second half be the sine curve wire.

Also, the magnetic field and the current through both the halves will be the same as it is acting on the entire loop.

Force acting on the first half i.e, the hemisphere, Fh  :

Force on the hemisphere will be acting upwards therefore, Fh is positive.

We have the radius of the hemisphere as R.  

Therefore,  

Fh = B*i*2R ….. (i)

Force acting on the second half i.e, the sine curve wire, Fs  :

The radius of the sine curve wire is R  

Force on the sine curve wire will be acting downwards therefore, Fs is negative.

Therefore,

Fs = - (B*i*2R) ….. (ii)

∴ The total force acting on the sinusoidal loop,

F =  Fh + Fs

Putting the values of Fh and Fs from (i) & (ii), we get

F = B*i*2R + (- B*i*2R) = B*i*2R - B*i*2R = 0

Hence the total force acting on the loop will be zero.

Hope it helps!!!!

Answer 2

Answer:

2BiR upwards

Explanation:

Read the question. It says find the net force on the sine curve!!! I was solving this just now and I skipped reading the question properly and spent like 10 minutes on this silly question xD

Anyway, I've attached the solution, hope it helps!