A rectangular wire loop (dimensions: h = 12.0 cm, w = 15.0 cm) is placed in a un

Question

A rectangular wire loop (dimensions: h = 12.0 cm, w = 15.0 cm) is placed in a uniform magnetic field B as shown in fig. a. The magnetic field B changes with time t as shown in fig. b. The resistance R of the loop is 0.5 ?.

a. (5) Determine the induced emf E on the loop for 0 < t < 0.1 s
b. (6) Determine the induced emf E' on the loop for 0.1 s < t < 0.2 s
c. (3) Calculate the induced current I during the time interval 0 < t < 0.1 s
d. (6) Use Lenz’s rule to determine the direction of the induced current during the time interval 0 < t < 0.1 s
e. (5) Determine the total charge Q that flows through a cross section of the loop wire during t.he time interval 0 < t < 0.2 s

Explanation / Answer

magnetic flux through the coil = B*A

induced emf = rate of change in flux

e = (d/dt)*(B*A)

e = A*(dB/dt)

A = area of the loop = w*h

a)

dB/dt = 0.15/0.1

emf = E = 0.12*0.15*(0.15/0.1) = 0.027 V

b)

from 0.1 < t < 0.2

dB/dt = 0

emf = E = 0

c)

i = E/R = 0.027/0.5 = 0.054 A

d)

E = -rate of change in fux

the magnetic filed increasing outwards , the magnetic flux also increases

the induced magneticfiled is inwards

the induced current is clockwise

e)

current flows only durin 0 to 0.1 s

Q = i*t = 0.054*0.1 = 0.0054 C

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