(10%) Problem 2: Two rectangular conducting loops are shown in the figure, separ

Question

(10%) Problem 2: Two rectangular conducting loops are shown in the figure, separated by a distance c = 3.5 cm. The loop on the left has a magnetic field passing through it, which is directed into the page and changes with time as B(t) = C1t, where C1 = 1.2 T/s. The dimensions of the two loops are given by a = 69 cm, b = 21 cm, and L = 68 cm. Both loops have the same resistance, R = 4 ?.

Randomized Variables a = 69 cm
b = 21 cm
c = 3.5 cm
L = 68 cm
C1 = 1.2 T/s
R = 4 ?

33% Part (a) Express the current, I1, that flows through the loop on the left in terms of the given quantities.

33% Part (b) Find the emf ?2, in volts, that is induced in the loop on the right by the changing magnetic field in the loop on the left.

33% Part (c) Now assume the magnetic field through the loop on the left changes in time as B(t) = C2t2, where C2 = 0.45 T/s2. Find the current I2, in amperes, through the loop on the right? Don't worry about the direction (so this should be a positive number).

(10%) Problem 2: Two rectangular conducting loops are shown in the figure, separated by a distance c = 3.5 cm. The loop on the left has a magnetic field passing through it, which is directed into the page and changes with time as B(t) = C1t, where C1 = 1.2 T/s. The dimensions of the two loops are given by a = 69 cm, b = 21 cm, and L = 68 cm. Both loops have the same resistance, R = 4 ?. Randomized Variables a = 69 cm b = 21 cm c = 3.5 cm L = 68 cm C1 = 1.2 T/s R = 4 ? 33% Part (a) Express the current, I1, that flows through the loop on the left in terms of the given quantities. 33% Part (b) Find the emf ?2, in volts, that is induced in the loop on the right by the changing magnetic field in the loop on the left. 33% Part (c) Now assume the magnetic field through the loop on the left changes in time as B(t) = C2t2, where C2 = 0.45 T/s2. Find the current I2, in amperes, through the loop on the right? Don't worry about the direction (so this should be a positive number).

Explanation / Answer

a)

i1=emf1/R

and emf1=A1*dB/dt

here,

B(t)=1.2t ==>dB/dt=1.2

A1=L*a

then

emf1=(L*a)*1.2

now,

i1=(L*a)*1.2/R

=(0.68*0.69)*1.2/4

=0.14076 A

=140.76 mA

b)

emf2=A2*dB/dt

=(L*b)*1.2

=0.68*0.21*1.2

=171.36 mV

c)

i2=emf2/R

and

emf2=A2*dB/dt

here

B(t)-0.45*t^2 ====>dB/dt=0.9t

then

emf2=(L*b)*0.9t

i2=(L*b)*0.9t/R

=(0.68*0.21)*0.9t/4

=0.03213*t A

=32.13*t mA

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