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Electromotive Force Problems

  1. May 1, 2005 #1
    Here are my homework problems. I did most of them, but I don't understand how to do the others.

    1. A rod of length 0.40 m moves in a magnetic field of magnitude B=1.2 T. The emf induced in the moving rod is found to be 2.40 V.
    a)what is the speed of the rod?
    b)if the total circuit resistance is 1.2 ohms, what is the induced current?
    c)What force (magnitude and direction) does the field exert on the rod as a result of this current?

    2. A rod of length 0.25 m moves with the constant speed of 6.0 m/s. The induced emf is found to be 3.0 V.
    a)what is the magnitude of the magnetic field?
    b)If a point called "a" was above a point called "b", which point is at a higher potential?

    3. A rod of lenght 0.15 m moves in a magnetic field directed into the plane of space. If B=0.5 T and the rod moves with the velocity 4 m/s.
    a)What is the motional emf induced in the rod?
    b)What is the potential difference between the ends of the rod?
    c)If a point called "a" was to the right of a point called "b", which point has a higher potential?

    4. A conducting rod AB makes contact with metal rails CA and DB. The apparatus is in a uniform magnetic field 0.5 T, perpendicular to the place of the diagram. The rod is 50 cm long.
    a)find the magnitude and direction of the emf induced in the rod when it is moving toward the right with a speed 4 m/s.
    b)If the resistance of circuit ABDC is 0.2 ohms (assumed constant), find the force required to maintain the rod in motion. Neglect friction.
    c)Compare the rate at which mechanical work is done by force (Fv) with the rate of development of heat in the circuit (i^2 R).

    5. A coil of 1000 turns enclosing an area of 20cm^2 is rotated from a position where its plane is perpendicular to the earth's magnetic field to one where its place is parallel to the field, in 0.02 seconds. What average emf is induced if the earth's magnetic field is 6 x 10^-5 T.

    6. A closely wound rectangular coil of 50 turns has dimensions of 12 cm x 25 cm. THe plane of the coil is rotated from a position where it makes an angle of 45 degrees with the magnetic field 2 T to a position perpendicular to the field in time t=0.1 seconds. What is the average emf induced in the coil?

    Here are the answers that I got:
    1) a) 5.00 m/s b) 2.00 Amps c) .960 N
    2) a) 2.00 T b) point A
    3) a) 3.00 V b) ??? c) ???
    4) a) .100 V b) .0125 N c) ???
    5) 6.00x10^-3 V
    6) 2.55 V

    Are my answers correct? Ask me if u want to know how I got these answers.
  2. jcsd
  3. May 1, 2005 #2
    EMF = dΦ/dt
    => EMF = BA/t
    consider in 1 second, the rod moving at speed v m/s,
    the area cut per second = length*v =0.4v

    so 2.4 = (1.2*0.4v)/1
    v = 5.0 m/s

    use EMF = IR

    F = BIL
    F = 1.2*0.4*2
    F = 0.960 N

  4. May 1, 2005 #3
    Can anyone help me with those other problems that I couldn't get the answers to, especially the potential difference problems.
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