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A few faraday law questions and emf, please help

  1. Sep 22, 2005 #1
    I got a few problems i am working on and getting stuck on. Here is what i got:
    Problem 1 A 34 turn circular coil of radius 3.20 cm and resistance 1.00 is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.0100t + 0.0400t2, where t is in seconds and B is in tesla. Calculate the induced emf in the coil at t = 6.00 s.

    So i do, (.032^2*pi)(1.5)(34)/6 and i get 27.3mV but appearantly this is wrong....

    Problem 2: An aluminum ring of radius r1 and resistance R is placed around the top of a long air-core solenoid with n turns per meter and smaller radius r2 as shown in Figure P31.7. Assume that the axial component of the field produced by the solenoid over the area of the end of the solenoid is half as strong as at the center of the solenoid. Assume that the solenoid produces negligible field outside its cross-sectional area. The current in the solenoid is increasing at a rate of I / t.

    a) What is the induced current in the ring? (Use u_0 for µ0, r_1 for r1, r_2 for r2, pi for , n, and R as necessary.)
    I say it is N(u-0/2*pi*r_1)/R but i am not sure

    (b) At the center of the ring, what is the magnetic field produced by the induced current in the ring? (Use u_0 for µ0, r_1 for r1, r_2 for r2, pi for , n, and R as necessary.)
    B = (u_0 N/r_2) but once again i am not sure.

    problem 3.A conducting rod of length moves on two horizontal, frictionless rails, as in Figure P31.20. A constant force of 1.00 N moves the bar at 2.00 m/s through a magnetic field B that is directed into the monitor.

    (a) What is the current through the 9.00 resistor R?
    (b) What is the rate at which energy is delivered to the resistor?
    (c) What is the mechanical power delivered by the force Faap?

    I am not sure how to do this one at all.

    problem 4. A long solenoid with 1500 turns per meter and radius 2.00 cm carries an oscillating current given by I = (3.00 A) sin(110t).
    (a) What is the electric field induced at a radius r = 1.00 cm from the axis of the solenoid?
    E = mV/m

    I know we got to do soemthing like E(2pi*r)= -piR^2u_0*N*I d/dt(sint)
    = E= (u_0*1500*3.00*omegaR^2/2r) * -cos(omega*t)

    problem 5
    The rotating loop in an ac generator is a square 12.0 cm on a side. It is rotated at 35.0 Hz in a uniform field of 0.800 T. Calculate the following quantities as functions of time t, where t is in seconds.
    a) the flux through the loop
    I assume i am going to use ba*cos theta?

    (b) the emf induced in the loop

    I assume i am going to do Ba(T)/t?

    (c) the current induced in the loop for a loop resistance of 2.00
    I assume i will do the emf/2?

    (d) the power delivered to the loop
    I am not sure how i would find this

    (e) the torque that must be exerted to rotate the loop
    I am also not sure how i would get this

    Problem 6
    A rectangular coil with resistance R has N turns, each of length and width w as shown in Figure P31.29. The coil moves into a uniform magnetic field with constant velocity . What are the magnitude and direction of the total magnetic force on the coil for the following situations? (Use N, B, w, v, and R as necessary.)


    a) The coil enters the magnetic field.
    F =
    (b) The coil moves within the field.
    F =
    (c) The coil leaves the field.
    F =

    Wouldn't it just be NBwv/R for all 3 since we are talkin about the magnetic force on teh coil? Or leaving the coil would be like -NNwv/R?
  2. jcsd
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