There is a region with a constant magnetic field 5.74T . The magnetic field is d

Question

There is a region with a constant magnetic field 5.74T . The magnetic field is directed out of the page. A conducting rod moves with a velocity of 1.81m/s , along a V shaped wire that is in the shape of a right triangle. At time = 0 s the rod is at the vertex of the triangle where the angle at the vertex is 20degrees . The right angle is where the conducting rod is. This means the rod is moving along the x axis and the rod is the y axis

Part A

What is the emf induced in the rod after it has moved from the vertex for a time of 12.2s ?

Part B

What is the current induced in the rod if the resistance is 4.62ohms ?

Part C

What is the power in the rod?

Explanation / Answer

area of triangle = (1/2)w h  

     h /w = tan20

         h = w tan20

area of the traingel = (1/2) w w*tan20=   0.181w2

the formula for induced emf is

emf induced = d? / dt = d(BA) / dt

                            = B dA/dt

                            = B d (0.181w2 ) / dt

   = 0.181 B  d(w2 ) / dt

                         = 0.181 B( 2 w dw/dt )

                         =  0.363 w Bv         

because dw/dt is v, the speed of the rod

at a time of 12.2sec     w = v t = 1.81 m/s ( 12.2 s) = 22.08 m

   emf induced =  0.363 (22.08 m)(5.74T) (1.81 m/s)   = 83.27 V

from the Ohms law

current is

I = emf induced / R = 83.27V/4.62ohms = 18.02 A

The formula for power is

P = IV = 18.02 A ( 83.27V) = 1501 W

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