A circular wire loop of resistance 1.00 $\varOmega$ and diameter 5.0 cm rotates about a horizontal axis while in a region having a 0.10 T magnetic field pointing in a horizontal plane at an angle of 35 degrees relative to the rotation axis.If the maximum current induced in the loop is 6.7 mA,what is the period of the rotation?
A)106 ms
B)164 ms
C)150 ms
D)93.2 ms
E)85.9 ms

Question

Quizplus · Accepted Answer

The maximum current induced in the loop is given by:$$I_{max}=\frac{\pi d^2 B \omega}{2R}$$where d is the diameter of the loop, B is the magnetic field strength, $\omega$ is the angular velocity of the loop, and R is the resistance of the loop.We can solve this equation for $\omega$:$$\omega=\frac{2RI_{max}}{\pi d^2 B}$$Substituting the given values, we get:$$\omega=\frac{2(1.00 \Omega)(6.7 \times 10^{-3} A)}{\pi (0.050 m)^2 (0.10 T)}=106 rad/s$$The period of the rotation is given by:$$T=\frac{2\pi}{\omega}$$Substituting the value of $\omega$, we get:$$T=\frac{2\pi}{106 rad/s}=106 ms$$Therefore, the correct answer is A.

A Circular Wire Loop of Resistance 1 Ω\varOmegaΩ And Diameter 5

A Circular Wire Loop of Resistance 1 $\varOmega$ And Diameter 5