A circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20

Question

A circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. (i) Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are parallel. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are perpendicular. A conducting bar moves along frictionless conducting rails connected to a 4.0 ohms resistor as shown above. The length of the bar is 1.60 m and B-field 2.20 T is applied perpendicular to the paper as shown. (i) What is the applied force required to the bar to the right with a constant speed of 6.0 m/s (ii) At what rate is energy dissipated in the 4.0 ohms resistor?

Explanation / Answer

1.a. magnetic flux = NAB cos theta

when theta = 0 deg, cos 0 =1,

flux will be maximum = NAB

= 1*3.14*0.1*0.1 * 0.2

=6.28*10^-3 T-m^2

b. as theta = 90 deg, cos90 =0, flux = zero 2. induced emf e= lvb = 1.6 * 6* 2.2 =21.12 volts

indiced current i = e/R = 21.12/4

= 5.28 Amps

now force F = ilB = 5.28 * 1.6 *2.2 = 18.58 N

power dissipated = i^2 R

= 5.28*5.28 * 4

=111.51 watts

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