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Homework Help: Electricity and magnetism. 2 questions

  1. Mar 7, 2006 #1
    A couple of questions.

    1. A capacitor of capacitance C is discharging through a resistor of resistance R. When will the energy stored be equal to half its initial value?

    My logic went like this:

    Energy in a capacitor (U) = Q^2/2C
    so: Q = (2CU)^0.5

    so therefore the charge when the energy is halved = (2C(U/2))^0.5 = (CU)^0.5

    so from Q=Q0*exp(-t/RC)
    (CU)^0.5 = (2CU)^0.5*exp(-t/RC)
    (CU)^0.5 = (2)^0.5*(CU)^0.5*exp(-t/RC)
    t = -RCln(1/(2)^0.5)

    and this second question I don't really follow at all.

    A particle of mass 6.0g moves at 4.0km/s in an xy plane, in a region of space with uniform magnetic field given by 5.0imT. At one instant when the particles velocity is directed at 37degrees counter clockwise from the positive x direction, the magnetic force on the particle is 0.48kN. What is the particles charge?

    I had a go using: F=qvBsin(x) (where x = angle) and got a charge of 0.039C. Is this the right way to go about it? Seems quite a large charge to me.
  2. jcsd
  3. Mar 8, 2006 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Your answer to the first question is correct.

    In the second, I think you are also right. I am assuming that i is the unit vector in the x direction and k is the unit vector in the z direction.

    So, [itex]\vec F = q\vec v \times \vec B = qvsin(x)B\hat k = .48N \hat k[/itex]

    [tex]\frac{F}{Bvsin(x)} = q [/itex]

    Plugging in the numbers:

    [tex]q = .48/(.005 * 4000 * .602) = .039 C[/tex]

    Think of the moving charge in terms of current: dQ/dt = I where dQ is the charge strung out over 4 km. The current is .039 amps. So this is equivalent to the force on a 4 km section of wire conducting a current of .039 amps

  4. Mar 8, 2006 #3
    So I wasn't far off? Thats not bad. I was just concerned because a mass was given in the question,but I didn't seem to use one.

    Ok. Thanks for that. Thats a bit more confidence in myself there!
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