A solenoid 4.0 cm in radius and 4.0 m in length has 8 000 uniformly spaced turns and carries a current of 5.0 A.Consider a plane circular surface (radius = 2.0 cm)located at the center 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

To find the magnetic flux through the circular surface we can use the formula for magnetic flux through a surface:
Φ = B⋅A
where Φ is the magnetic flux, B is the magnetic field, and A is the area of the surface.
Inside the solenoid, the magnetic field is approximately uniform and is given by:
B = μ₀nI
where μ₀ is the permeability of free space, n is the number of turns per unit length (in this case, n = 8000/4 = 2000 turns/m), and I is the current.
Substituting the given values, we get:
B = 4π×10^-7 × 2000 × 5 = 0.01 T
The area of the circular surface is A = πr² = π(0.02²) = 1.2566×10^-3 m²
Substituting the values for B and A, we get:
Φ = (0.01 T) × (1.2566×10^-3 m²) = 1.2566×10^-4 Wb = 16 μWb
Therefore, the correct answer is (B) 16 μWb.

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