Question

A 2 m long solenoid with radius 2 cm and 2000 turns has a another solenoid of 1000 turns wound closely near its mid-point. the mutual inductance of solenoids is

(a) 0 8. mh
(b) 1 6. mh
(c) 3 2. mh
(d) 6 4. mh

Answer 1

From the options provided the the mutual inductance of solenoids is ) 1 6. mh. Option B

To find the mutual inductance of two solenoids, we use the formula:

M = (μ₀ * N₁ * N₂ * A) / ℓ

In this example, we have a 2 meter long coil with a diameter of 2 centimeters and 2000 loops of wire. Another coil with 1000 loops is wound tightly near its middle. We need to figure out how much they affect each other.

The size of the area when you cut through an object.

A = π * r² = π * (0.02 m)² = 0.00126 m²

ℓ = 2 m / 2 = 1 m

Now, we can put the numbers into the equation to figure out the mutual inductance.

M = (μ₀ * N₁ * N₂ * A) / ℓ

= (4π * 10^-7 * 2000 * 1000 * 0.00126) / 1

= 1.006 mH (rounded to 3 significant figures)

So, the answer is choice (b) 1. 6mH

The value closest to the calculated number is (b) 1. 6 millihenries