A circular wire loop of resistance R = 1.0 $\varOmega$ rotates with period 150 ms 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 diameter of the loop?
A)6.0 cm
B)2.8 cm
C)5.0 cm
D)4.2 cm
E)6.5 cm

Question

Quizplus · Accepted Answer

The maximum current induced in the loop is given by:$$I_{max} = \frac{BA\omega}{R}$$where:* $I_{max}$ is the maximum current induced in the loop* $B$ is the magnetic field strength* $A$ is the area of the loop* $\omega$ is the angular velocity of the loop* $R$ is the resistance of the loopWe are given that:* $I_{max} = 6.7 mA = 6.7 \times 10^{-3} A$* $B = 0.10 T$* $R = 1.0 \Omega$* $\omega = \frac{2\pi}{T} = \frac{2\pi}{150 \times 10^{-3} s} = 41.89 rad/s$Solving for $A$, we get:$$A = \frac{I_{max}R}{B\omega} = \frac{(6.7 \times 10^{-3} A)(1.0 \Omega)}{(0.10 T)(41.89 rad/s)} = 1.6 \times 10^{-3} m^2$$The area of a circle is given by:$$A = \pi r^2$$where $r$ is the radius of the circle. Solving for $r$, we get:$$r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{1.6 \times 10^{-3} m^2}{\pi}} = 0.04 m = 4.0 cm$$Therefore, the diameter of the loop is:$$d = 2r = 2(0.04 m) = 0.08 m = 8.0 cm$$The correct choice is A.

A Circular Wire Loop of Resistance R = 1 Ω\varOmegaΩ Rotates with Period 150 Ms About a Horizontal Axis While

A Circular Wire Loop of Resistance R = 1 $\varOmega$ Rotates with Period 150 Ms About a Horizontal Axis While