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Question

A square of side of 2.0 m is placed in a uniform magnetic field B=2.0 T in a direction perpendicular to the plane of the square inwards. Equal current i=3.0 A is flowing in the directions shown in figure. Find the magnitude of magnetic force acting on the loop ABCD.



A
182 N
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B
272 N
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C
362 N
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D
162 N
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Solution

The correct option is C 362 N

​​​​​​From the above figure, it is clear that , it is not an example of closed loop. Rather it can be treated as combination of the following parts,


As, F=I(L×B)

where, L is effective length.

All three segments have same effective length as AD=22 m [AD=AC2+CD2]
with some direction from AD

Since, Force on ACD=Force on AD=Force on AED
Net force on loop =3FAD

Fnet=3i[L×B]

=3i[AD×B]

=3×3[(AD)Bsin90]

=3×3[22×2]

Fnet=362 N

Hence, option (c) is the correct answer.

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