a circular loop of radius 29cm is located in the plane of the paper inside a hom

Question

a circular loop of radius 29cm is located in the plane of the paper inside a homogenous magnetic field of 0.1T pointing into the paper. it is connected in series with a resistor of 221 ohm. the magnetic field is now increased at a constant rate by a factor of 2.5 in 13s.

a)calculate the magnitude of the induced emf in the look during this time.

b) calculate the current induced in the loop during that time

c) calculate the average induced voltage when the magnetic field is constant at 0.25 T while the loop is pulled horizontally out of the magnetic field region in 9.3s.

thank you

Explanation / Answer

a)

A=pi*r^2 =pi*0.29^2

A=0.2642 m^2

initial magnetic field

B1 =0.1 T

final magnetic field

B2=2.5*0.1 =0.25 T

change in magnetic field

dB =B2-B1 =0.15 T

Induced emf

E=A(dB/dt)

E=0.2642*(0.15/13)

E=3.05*10^-3 V or 3.05 mV

b)

I=E/R =3.05*10^-3/221

I=1.38*10^-5 A or 13.8 uA

c)

E=B(dA/dt)

E=0.25*0.2642/9.3

E=7.1*10^-3 V or 7.1 mV

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