Problem 21.15 Part of a single rectangular loop of wire with dimensions shown in

Question

Problem 21.15

Part of a single rectangular loop of wire with dimensions shown in the figure (Figure 1) is situated inside a region of uniform magnetic field of 0.808T . The total resistance of the loop is 0.684? .

Part A

Calculate the force required to pull the loop from the field (to the right) at a constant velocity of 3.69m/s . Neglect gravity.

Figure 1 of 1

Problem 21.15

Part of a single rectangular loop of wire with dimensions shown in the figure (Figure 1) is situated inside a region of uniform magnetic field of 0.808T . The total resistance of the loop is 0.684? .

Part A

Calculate the force required to pull the loop from the field (to the right) at a constant velocity of 3.69m/s . Neglect gravity.

Figure 1 of 1

Explanation / Answer

emf induced = d(BA)/dt = B dA/dt = B(L x )/dt

emf induced = V = 0.35 B dx/dt = L B v

Here it is given that

V = i R = L B v

i = L B v / R

Since current is flowing in the loop

Force on the conductor

= B i L = B (B L v / R) L = B^2 L^2 v / R

In orde to pull at constant velocity , Force applied should be same

Hence

F =  B^2 L^2 v / R = 0.808^2 x 0.35^2 x 3.69 / 0.684 = 0.431 N

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Answer

F = 0.431 N

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