Question

A long solenoid of radius 1 mm has 100 turns per mm. If 1 A current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:

• A. 6.28 x 10^-2 T
• B. 12.56 x 10^-2 T
• C. 12.26 x 10^-4 T
• D. 6.28 x 10^-4 T

Answer 1

The Correct Option is B

To find the magnetic field strength at the center of a long solenoid, we can use the formula:

B = μ₀nI

where:

• B is the magnetic field inside the solenoid (in Tesla).
• μ₀ is the permeability of free space, approximately 4π x 10^-7 Tm/A.
• n is the number of turns per unit length of the solenoid (in turns/m).
• I is the current flowing through the solenoid (in Amperes).

Given data:

• Radius of solenoid = 1 mm (not needed in calculation as it doesn't affect the magnetic field inside for an ideal solenoid).
• Number of turns per mm = 100 turns/mm.
• Current, I = 1 A.

First, convert the number of turns per mm to turns per meter:

n = 100 turns/mm = 100,000 turns/m

Plug the values into the formula:

B = (4π x 10^-7 Tm/A)(100,000 turns/m)(1 A)

Simplify the equation:

B = 4π x 10^-7 x 100,000 T

B = 4π x 10^-2 T

Calculating:

B ≈ 12.56 x 10^-2 T

Thus, the magnetic field strength at the center of the solenoid is 12.56 x 10^-2 T.