Magnetic Field of Wire

There is a region with a constant magnetic field 5.32T . The magnetic field is directed out of the page. A conducting rod moves with a velocity of 2.33m/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 is16 degrees . 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 6.3s

Part B) What is the current induced in the rod if the resistance is 4.82ohms ?

Part C) What is the power in the rod?

At time $t=6.3$ sec the length of $x= v*t =2.33*6.3 =14.679 m$

$x/sin(74) =y/sin(16)$

the length of rod is

$y = x*sin(16)/sin(74) =4.209 m$

The area of triangle is $S =x y/2 =30.893 m^2$

The variation of flux is

$Phi – S*B = 164.35 Wb$

The induced voltage is

$U = -Phi/t = – 164.35/6.3 =26.087 V$

(the current rotates clockwise in the circuit in the figure)

Current is

$I = U/R =26.087/4.82 =5.412 A$

Power is

$P = U*I = 141.19 W$