There is a region with a constant magnetic field 6.31T . The magnetic field is d

Question

There is a region with a constant magnetic field 6.31T . The magnetic field is directed out of the page. A conducting rod moves with a velocity of 1.58m/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.

What is the emf induced in the rod after it has moved from the vertex for a time of 10.9s ?

What is the current induced in the rod if the resistance is 5.31ohms ?

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 10.9 sec     w = v t = 1.58 m/s ( 10.9 s) = 17.22 m

   emf induced =  0.344 (17.22m)(6.31T) (1.58 m/s)   = 59 V

from the Ohms law

current is

I = emf induced / R = 59 V/5.31ohms = 11.12 A

The formula for power is

P = IV = 11.12 A ( 59 V) = 656.2 W

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