There is a region with a constant magnetic field 5.81T . The magnetic field is d

Question

There is a region with a constant magnetic field 5.81T . The magnetic field is directed out of the page. A conducting rod moves with a velocity of 1.65m/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 19degrees . 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 6.2s ?

Part B

What is the current induced in the rod if the resistance is 4.48ohms ?

Part C

What is the power in the rod?

Explanation / Answer

area of triangle = (1/2)w h  

     h /w = tan19    

         h = w tan19

area of the traingel = (1/2) w w*tan19=   0.172 w2

the formula for induced emf is

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

                            = B dA/dt

                            = B d (0.172w2 ) / dt

   = 0.172 B  d(w2 ) / dt

                         = 0.172 B( 2 w dw/dt )

                         =  0.344 w Bv         

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

at a time of 6.2sec     w = v t = 1.65 m/s ( 6.2 s) = 10.23 m

   emf induced =  0.344 (10.23m)(5.81T) (1.65 m/s)   = 33.73 V

from the Ohms law

current is

I = emf induced / R = 33.73 V/4.48ohms = 7.53 A

The formula for power is

P = IV = 7.53A ( 33.73V) = 254W

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