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Question

A long copper wire is wound in the form of a coil of radius r. A current of 2 A is passed through this coil and the magnetic induction at the centre of this coil is noted. The same wire is now folded end to end and coil of the same radius r is prepared and the same current is passed through it. The magnetic induction at the centre:
  1. will be doubled
  2. will be halved
  3. will remain same.
  4. will drop to zero

A
will drop to zero
B
will be doubled
C
will be halved
D
will remain same.
Solution
Verified by Toppr

Answer is B.

A solenoid is a coil of wire designed to create a strong magnetic field inside the coil. By wrapping the same wire many times around a cylinder, the magnetic field due to the wires can become quite strong. The number of turns N refers to the number of loops the solenoid has. More loops will bring about a stronger magnetic field.
The magnetic field inside a solenoid is proportional to both the applied current and the number of turns per unit length. There is no dependence on the diameter of the solenoid, and the field strength doesn't depend on the position inside the solenoid, i.e., the field inside is constant.
In this case, A long copper wire is wound in the form of a coil of radius r and later the same wire is now folded end to end and coil of the same radius r is prepared and the same current is passed through it.
Here, the strength of the magnetic field is decreased as the length of the solenoid is also decreased. That is, the magnetic induction at the center will be halved as the length of the solenoid and magnetic field strength are directly proportional.

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