104. A current carrying circular loop having n number of turns per unit length has a current I through I it. If the current through it and the number of turns per unit length are doubled, then the magnetic field at the centre of the loop will:
(a) remain same.
(b) increase by four times.
(c) increase by two times.
(d) decrease by two times.
Answers
Answer:
Increase by four times.
Explanation:
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A circular loop of wire is a solenoid.
The magnetic field strength inside a solenoid is given by:
B = μ0nI (inside a solenoid) where
n is the number of loops per unit length of the solenoid,
I is the current flowing,
μ0 is known as the magnetic constant or the permeability of free space.
Further, n = N/l, with N being the number of loops and l the length.
It is given that the current flowing and the number of turns per unit length are doubled, it means that the magnetic field strength becomes four times.
To simplify it further, since B = μ0nI before the change in a number of turns and current.
When n => 2n and I => 2I,
The equation becomes μ0(2n)(2I).
Hence, B becomes 4B after a double increase in the number of turns and the current flowing through it.