In the figure, a conducting rod of length L = 26.0 cmmoves in a magnetic field B

Question

In the figure, a conducting rod of length L = 26.0 cmmoves in a magnetic field B  of magnitude 0.450 Tdirected into the plane of the figure. The rod moves with speed v = 5.00 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? Express your answer in volts to at least three significant figures.

3) What is the magnitude E of the motional emf induced in the rod? Express your answer in volts to at least three significant figures.

Explanation / Answer

given that

L = 26 cm = 0.26 m

B = 0.45 T

v = 5 m/s

when the rod is in motion charges experience magnetic force in presence of magnetic field

Fb = q*(vxB)

velocity is in -y direction and field is inside the plane

so, Fb = q*v*B

there is attractive coulombic force between charges which is equal to megnetic force

q*v*B = q*E

E = v*B

E = 5*0.45 = 2.25 V/m

(b)

we know that

emf V = E*d

V = 2.25*0.26 = 0.585 V

(b)

motional emf induced in the rod = v*B*L

V = 5*0.45*0.26

V = 0.585 V

answer

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