A square loop of Cu wire 4.00cm on an edge is lying on a horizontal table. An el

Question

A square loop of Cu wire 4.00cm on an edge is lying on a horizontal table. An electromagnet above the square loop is turned on to produce a magnetic field. The magnetic field, directed downward toward the table and at an angle of 60 degrees from the surfaceof the table, goes through the square loop of Cu wire. (Copper wire for this problem: radium 1.02mm and resistivity of copper is 1.70e-8ohms*m)

Find:

a) the induced emf in the loop if the magnetic field due to the electromagnet increases from 0.00T to 0.500T in 0.200s

b) what is the current in teh square loop?

c) what is the power loos in the loop?

Explanation / Answer

a) Surface of loop is S =4*4 =16 cm^2 =16*10^-4 m^2

Perpendicular component of B to surface of loop is Bn = B*sin(alpha),   alpha =60 degree

flux of B through surface is Fi = Bn*S = B*S*sin(60)

Induced voltage is

Vind =-d(fi)/dt = 0.5*16*10^-4*sin(60)/0.2 =3.46*10-3 V =3.46 mV

b) length of loop L =4*4 =16 cm

Resistance of loop R = ro*L/S =1.7*10^-8*0.16/(pi*0.00102^2) =8.32*10^-4 ohm

I = Vind/R = 3.46*10^-3/8.32*10^-4 =4.158 A

c) Power loss is P = U*I =0.0144 W

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