The electric current in a circular coil of four turns produces a magnetic induction of at its center. The coil is unwound and rewound into a circular coil of single turn. The magnetic induction at the center of the coil by the same current will be:
Correct answer:C
Standard Method
Given: Initial coil has turns and magnetic induction at the center is . The wire is rewound into a single-turn circular coil with the same current.
Find: The new magnetic induction at the center.
For a circular coil of turns,
Initially,
When the four-turn coil is unwound and rewound into a single turn, the total length of wire remains the same. Hence the circumference of the new coil becomes times the original circumference, so the new radius is
For the new single-turn coil,
Substituting ,
Now compare with the initial field:
Therefore,
So, the magnetic induction at the center becomes . Therefore, the correct option is C.
The solution marks B, but its own working gives , which matches option C.
Using the field formula for a single-turn coil but forgetting that the radius changes when the same wire is rewound. The wire length stays constant, so the new radius becomes . Always apply length conservation before comparing fields.
Assuming the magnetic field depends only on the number of turns. It depends on both and through . Reducing turns from to and increasing radius both reduce the field.
Directly trusting the listed answer key without checking the solution steps. Here, the key shows B, but the working clearly gives . Verify the final value from the derivation and then match it to the options.
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