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

We can use Faraday's law to relate the induced electric field to the rate of change of magnetic flux through a closed loop around the solenoid:

$E = -\frac{d\Phi_B}{dt}$

Since the magnetic field is uniform within the solenoid, we can write the flux in terms of the field strength and the cross-sectional area:

$\Phi_B = B(t) A$

where $A = \pi r^2$ is the cross-sectional area of the solenoid.

Thus,

$E = -\frac{d}{dt}(B(t) A) = -\frac{d}{dt}(5.0t \pi r^2) = -5.0\pi r^2$

We can now solve for the radius of the solenoid:

$r = \sqrt{\frac{1.1}{5.0\pi}}\approx 0.94 m$

Therefore, the answer is C.

For a Long Ideal Solenoid Having a Circular Cross-Section,the Magnetic