(A) Find the magnetic flux through a circular loop 4.8 c m in diameter oriented

Question

(A)

Find the magnetic flux through a circular loop 4.8cm in diameter oriented with the loop normal at 46? to a uniform 50mT magnetic field.

(B)

A conducting loop of area 210cm2 and resistance 15? lies at right angles to a spatially uniform magnetic field. The loop carries an induced current of 335mA .

At what rate is the magnetic field changing?

(C)

The magnetic field inside a 21cm -diameter solenoid is increasing at the rate of 2.4T/s .

How many turns should a coil wrapped around the outside of the solenoid have so that the emf induced in the coil is 20V ?

(D)

A 6-turn coil 1.0cm in diameter is rotated at 11rev/s about an axis perpendicular to a uniform magnetic field. A voltmeter connected to the coil through rotating contacts reads a peak value of 360?V .

What is the magnetic-field strength?

Explanation / Answer

A)

r = d/2 = 4.8/2 = 2.4 cm = 0.024 m

magnetic flux = B*A*cos(46)

= 50*10^-3*3.14*0.024^2*cos(46)

= 6.28*10^-5 weber

B) induced emf = A*dB/dt

i = emf/R

i = (A/R)*dB/dt

==> dB/dt = i*R/A = 0.355*15/210*10^-4 = 253.57 Tesla/s

C) r = d/2 = 21/2 = 10.5 cm = 0.105 m

A = pi*r^2 = 0.0346 m^2

induced emf = N*A*dB/dt

==> N = emf/(A*dB/dt)

= 20/(0.0346*2.4)

= 240.72 turns

D) w = 11*2*pi/60 = 1.151 rad/s

emf_max = N*B*A*w

==> B = emf/N*A*w)

= 360*10^-6/(6*3.14*0.05^2*1.151)

= 6.64*10^-3 T

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