A single rectangular loop of wire with the dimensions in the figure is situated

Question

A single rectangular loop of wire with the dimensions in the figure is situated so that part is inside a region of uniform magnetic field of 0.450 T and part is outside the field. the total resistance of the loop is 0.230 ohms.

a) calculate the force required to pull the loop from the field ( to the right) at constant velocity of 3.40 m/s. Neglect gravity.

b) what is the magnitude and direction of the induced current through the loop?

c) how far from the vertical portion of the current will the magnetic field be zero momentarily? would that happen on the left of right side of the vertical current. ignore horizontal currents.

please provide clear, step by step solutions. thank you!

Explanation / Answer

magnetic field, B=0.45 T

total resistance, R=0.23 ohms

velocity, v=3.4 m/sec

a)

F=i*l*B

F=(emf/R)*l*B

F=(l*V*B/R)*(l*B)

F=v*l^2*B^2/R

F=3.4*(0.35)^2*(0.45)^2/(0.23)

F=0.367 N

b)

induced current, i=emf/R

i=l*v*B/R

i=(0.35*3.4*0.45)/(0.23)

i=2.33 A

direction is clock wise

c)

if the loop moves right side completely, flux through loop become zero,

vertical current portion of the left side of the loop   decreases

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