A solenoid 4.0 cm in radius and 4.0 m in length has 8000 uniformly spaced turns and carries a current of 5.0 A.Consider a plane circular surface (radius = 2.0 cm) located at the centre of the solenoid with its axis coincident with the axis of the solenoid.What is the magnetic flux through this surface? (1 Wb = 1 T . m2)
A)63 $\mu$Wb
B)16 $\mu$Wb
C)0.25 mWb
D)10 $\mu$Wb
E)5.0 $\mu$Wb

Question

Quizplus · Accepted Answer

The magnetic flux through a surface is given by
Φ = BA
where B is the magnetic field at the center and A is the area of the surface.

For a solenoid, the magnetic field at the center is given by
B = μ₀nI
where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current.

Using the given values, we have
n = N/L = 8000/4 = 2000 turns/m
B = (4π×10⁻⁷ T•m/A)(2000 turns/m)(5 A) = 4×10⁻³ T

The area of the circular surface is A = πr² = π(0.02 m)² = 1.26×10⁻⁴ m²

Therefore, the magnetic flux through the surface is
Φ = BA = (4×10⁻³ T)(1.26×10⁻⁴ m²) = 5.04×10⁻⁷ Wb
or 16 μWb (since 1 Wb = 10⁶ μWb)

So the answer is B.

A Solenoid 4 μ\muμ Wb B)16 μ\muμ Wb C)0 μ\muμ Wb E)5 μ\muμ Wb

A Solenoid 4 $\mu$ Wb
B)16 $\mu$ Wb
C)0 $\mu$ Wb
E)5 $\mu$ Wb