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See attached document for questions.

Magnetics & Induction

4a1. Find the direction and magnitude of force exerted on an electron with initial velocity (= 100 m/s) along +x axis, if
o

the magnetic field (2 T) is pointing at +30

angle from +X axis, in the XY plane.

-19
Hint: F = (-1.6x10

C)(100 m/s)(2T)sin(30 ) = N, along the - z direction, i.e. into the paper.

4a2. Find the direction and magnitude of force exerted on an electron with initial velocity (= 1000 m/s) along +x axis,
if the magnetic field ( 2 T) is pointing in +z direction, i.e. out of the paper.

4b1. A proton with velocity ( 5x10

m/s) in +y direction, enters a region where B ( 0.1 T) is in +z direction. Calculate

the radius of resulting circular path. Use [5].

4b2. What must have been the accelerating voltage, if above mentioned proton motion were a part of the mass-
+
spectrometer described in Module4b? How strong a B is needed if the detected ion is charged iron (Fe ) instead? Use
[6], and then use [7].

4c1. A 2 m long wire conducting 10 A in +x direction, is placed in 0.1 T magnetic field pointing in +z direction. Calculate the magnitude and the direction of the force.

4c2. A square coil (A = 0.01 sq. m.) of 100 turns is placed horizontally, in a magnetic field ( 1 T) pointing towards right. Calculate the total force on the coil, if the current is 10 A.

4d1. A square coil (A = 0.01 sq. m.) of 100 turns is placed horizontally, in a magnetic field ( 1 T) pointing towards right. Calculate the torque on the coil, if the current is 10 A. Draw a diagram, and use [11].

4d2. Calculate the average torque on the coil as it turns through quarter turn, by taking average of a table of 10 values
o

of sin function at 10

interval. Set up an excel spreadsheet with a column with angles from 0o to 90o. If the arrangement

is turned into a DC motor, calculate the power if the rotor is spinning at 3600 RPM. (Hint: Poweraverage = average*)

4e1. Calculate the B field of a straight conductor carrying 10 A current at r = 0.01 m.

4e2. Two wires (each of length L = 1 m ) are placed , along +Z, parallel to each other at distance d= 0.1m. They carry current I1 = 10 A and I2 = 5 A respectively. See section 19.8 in Serway Text 7th edition.

Draw a diagram.

(1) Calculate the B the field at the location of wire 2 produced by the wire 1.
(2) Calculate the force on the wire 2 due to the B field produced by 1, calculated above. (3) Likewise calculate the force on the wire 1 due to the field produced by wire 2.
(4) What would happen if the direction of current in both wires were to be reversed?
(5) What would happen if the direction of current is reversed in only one wire?

(Continued.....)

4f1. A bar of 1 m length aligned in y direction moves in +x direction at 10 m/s, in space where B = 1 T pointing in the - z direction. Calculate the motional EMF.

4f2. If the bar, in 4f1 above, is a part of a circuit (shown in the diagram below) with a light bulb of 10  resistance, what would be the induced current?

I
Y

v

B
X

4f3. Show that the electrical power dissipated in the light bulb in 4f2 is equal to the mechanical power supplied by force which moves the bar.
(Hints: P = I2R. Calculate the magnetic force on the bar, then use P = Fv)

4g1. Verify equation [19] E = -/t , for the 4f2 above, i.e. calculate the rate of change of flux.

4g2. A square coil (A = 0.01 m ) of 100 turns is in the xz plane, where the B field of 10 T is pointing in the +x direction. Calculate average induced EMF if the coil is rotated by 10 degrees (about z axis) in 0.1 s. (An external agent rotates the coil, and EMF is produced: An example of Electrical Generator )

4h1. Consider a loop in xy plane, in magnetic field pointing in the -z direction. What would be the direction of the induced current if the original B field were decreasing?

4i1. Calculate the amplitude of the AC voltage generated by an electric generator if the shaft is rotating at 60 RPM, and A = 1 m , B = 1 T, N = 1000.

4i2. The coil of a AC motor has resistance of 4 . Assume that under operating condition the rms value of the back EMF produced is 118 V, when it is drawing power from 120 V wall outlet. Calculate the startup current, and the operating current.

4j1. A 100 turn solenoid`s dimensions are: l = 0.2m, r = 0.025m. Calculate the L. {n = N/ l }

4j2. Calculate the induced voltage if the current through above solenoid is changing at the rate of 100 A/s.

4j3. Calculate the stored magnetic energy in the above solenoid if the current is 5 A at a given time.

4j4. Calculate mutual inductance between two coils if 50 A/s rate of change of current through one coil induces 2 volts across another coil.

4j5. (a) Explain why the transmission lines have high voltage.

(b) Explain why high voltage is not usually used near the point of use (i.e. home, industry).