Induced electric fields: For a long ideal solenoid having a circular cross-section, the magnetic field strength within the solenoid is given by the equation B(t) = 5.0t T, where t is time in seconds. If the induced electric field outside the solenoid is 1.1 V/m at a distance of 2.0 m from the axis of the solenoid, find the radius of the solenoid.
A) 0.30 m
B) 77 m
C) 0.94 m
D) 9.0 m

Question

Quizplus · Accepted Answer

The induced electric field at a distance r from the axis of the solenoid is given by:
E(t) = -dΦ/dt = -d(Bπr²)/dt = -πr²dB/dt
where Φ is the magnetic flux and negative sign indicates that the induced electric field is in the opposite direction to the change in magnetic flux.

We know that B(t) = 5.0t T
So, dB/dt = 5.0 T/s

At a distance of 2.0 m, E(t) = 1.1 V/m
So, 1.1 = π(2.0)²(5.0)
Solving for π, we get π ≈ 3.14

Substituting the value of π and dB/dt in the equation for E(t), we get:
1.1 = 3.14r²(5.0)
Solving for r, we get r ≈ 0.94 m

Therefore, the radius of the solenoid is 0.94 m, which is option C.

Induced Electric Fields: for a Long Ideal Solenoid Having a Circular