Question

In the figure, a conducting rod of length L = 33.0 cm moves in a magnetic field B? of magnitude 0.550 T directed into the plane of the figure. The rod moves with speed v = 4.00 m/s in the direction shown.

1. When the charges in the rod are in equilibrium, what is the magnitude E of the electric field within the rod?  

2.What is the magnitude Vba of the potential difference between the ends of the rod?

3.What is the magnitude E of the motional emf induced in the rod?

Answer 1

1)

when the rod is in motion charges experience magnetic force in presence of magnetic field and  
according to Force(magnetic) = q*[cross product of velocity and field]
if velocity is on -ve y-axis and field inside the plane then by Right hand Screw rule positive charges experience force towards point P and negative charges accumulate at point A and hence naturally their is attractive coulombic force between charges so in steady condition these forces balance each other and Hence
q*v*B = q*E
E = v*B
E = 4*0.550 = 2.2V

2)

emf V = E*d
d = 33cm = 0.33m
V = 2.2*0.33
V = 0.726V

3)

E = v*B
E = 4*0.550 = 2.2V