The dimensions of the rectangular loop of wire in(Figure 1) are = 400 mm and w =

ID: 1444473 • Letter: T

Question

The dimensions of the rectangular loop of wire in(Figure 1) are = 400 mm and w = 120 mm. The mass of the loop is 10 g , its resistance is6.0 V/A ,and before entering the magnetic field shown the loop is moving at a constant speed vi. The magnetic field magnitude is 5.0 T, and the loop's area vector is parallel to the field direction.

How many seconds after the leading edge of the loop enters the magnetic field is the loop's speed half its initial value? Ignore any friction effects.

t = _____________s

t x x Binto the figure

Explanation / Answer

induced emf = B w v

power dissipated = e^2 / R = B^2 w^2 v^2 / R

and Power, P = F.v

F = - B^2 w^2 v / R

m dv/dt = - B^2 w^2 v / R

dv/v = - (B^2 w^2 / m R) dt

integrating

ln v = - B^2 w^2 t / mR

v is from v to 0.5v

ln(0.5v) - ln v = - B^2 w^2 t / mR

ln(0.5v /v) = ln(0.5) = - B^2 w^2 t / mR

ln(0.5) = - (5^2 x 0.120^2 x t) / (10 x `10^-3 x 6 )

t =0.12 sec

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The dimensions of the rectangular loop of wire in(Figure 1) are = 400 mm and w =

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