PLEASE HELP ME A uniform field varies according to B(t) = 4.0 + 2.0 t + 0.5 t^2

Question

PLEASE HELP ME

A uniform field varies according to B(t) = 4.0 + 2.0 t + 0.5 t^2 (B is in tesla and t in seconds). A wire loop with sides of length 4 cm is present as shown. Its total resistance is 10 ohm. (a) What is the direction of the induced current in the loop? (b) What is the induced EMF in the loop at t = 0 s? What is the current? (c) What is the EMF and current at t = 10 s? Two rods (shown in black in the figure) each have length L and resistance R. They are in a magnetic field, L going into the page. The rods are resting on two rails (shown in grey) that have negligible resistance. Suppose the left rod is fixed in place and the right rod is moved at constant velocity y to the left. What external force ? must be applied to the right rod to maintain its velocity? (If a current is induced, there will be a force on it due to the magnetic field. Thus, for the rod to move at constant velocity, there must be some external force balancing the magnetic force.) Suppose both rods move at constant velocity y to the right with a distance D between them. Now what external force F must be applied to both rods to maintain their velocities?

Explanation / Answer

a)

Into the page

b)

Area of square loop

A=0.042=1.6*10-3 m2

Rate of change of magnetic field

dB/dt =2+t

at t=0

Induced emf

E=A(dB/dt) =(1.6*10-3)(2+0)

E=3.2*10-3 Volts or 3.2 mV

Induced current in the loop

I=E/R =(3.2*10-3)/10

I=3.2*10-4 A or 0.32 mA

c)

at t=10 s

Induced emf

E=(1.6*10-3)(2+10)

E=1.92*10-2 Volts or 19.2 mV

Current

I=E/R =1.92*10-2/10

I=1.92*10-3 A or 1.92 mA

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