
Figure shows a conducting loop placed in a uniform magnetic field (strength ) perpendicular to its plane. The part is the (three-fourth) portion of the square of side length . The part is a circular arc of radius . The points and are connected to a battery which supplies a current to the circuit. The magnetic force on the loop due to the field is:
A.
B.
C.
D.

Answer
504.3k+ views
Hint: Since, the current through the loop splits into to part, one flows through and other through . During the current flow, there will be some force generated. To find the total force generated in the loop , the force generated on loops and are calculated. Since, the two currents travel the same distance in the magnetic field, the current gets added. Thus, the total force can be calculated.
Useful formula:
Relation between force, current and magnetic field will be given by,
Where, is the force on the conductor, is the magnetic field, is the current flows through the conductor and is the length of the conductor.
Complete Step by step solution:
Assume that,
The current through the loop is
The current through the loop is
The length where the current flow in loop is
The length where the current flow in loop is
The force generated on the loop ,
Where, is the force generated on loop , is the current flows through the loop and is the length of the loop .
The force generated on the loop ,
Where, is the force generated on loop , is the current flows through the loop and is the length of the loop .
Hence, the total force on loop is the sum of the force on loop and the force on loop ,
Substitute the values of (1) and (2) equation (1),
Since, the current travels the same length in the loops and ,
Hence,
The total current,
Thus,
Hence, the option (B) is correct.
Note: In the loop , even the structure of the loops and may vary, but the current flows through the loops in the uniform magnetic field travels the same distance in both the loops. A force will be generated in the current carrying conductor placed in a uniform magnetic field, this is the statement of Faraday’s law of induction. The force generated in the loop , is the sum of the force generated in loops and .
Useful formula:
Relation between force, current and magnetic field will be given by,
Where,
Complete Step by step solution:

Assume that,
The current through the loop
The current through the loop
The length where the current flow in loop
The length where the current flow in loop
The force generated on the loop
Where,
The force generated on the loop
Where,
Hence, the total force on loop
Substitute the values of (1) and (2) equation (1),
Since, the current travels the same length in the loops
Hence,
The total current,
Thus,
Hence, the option (B) is correct.
Note: In the loop
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