Question

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to ______.

Options

• B

• 2 B

• 4 B

• `"B"/2`

Answer 1

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to B.

Explanation:

Magnetic field due to solenoid is given by

B = `mu_0"nI"` ⇒ B ∝ nI

⇒ `"B"_2/"B"_1=("n"_2"I"_2)/("n"_1"I"_1)`

⇒ B₂ = `("n"_2"I"_2)/("n"_1"I"_1)xx"B"_1`

⇒ B₂ = `1/2xx2xx"B"_1`

∴ B₂ = B