A metallic circular plate with radius r is fixed to a tabletop. An identical circular plate supported from above by a cable is fixed in plac

Question

A metallic circular plate with radius r is fixed to a tabletop. An identical circular plate supported from above by a cable is fixed in place a distance d above the first plate. Assume that d is much smaller than r. The two plates are attached by wires to a battery that supplies voltage V.

Required:
a. What is the tension in the cable?
b. Compute the energy stored in the electric field after the top plate was raised.

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King 2 months 2021-07-30T01:33:56+00:00 1 Answers 2 views 0

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    2021-07-30T01:35:29+00:00

    Answer:

    A) F = V²E_o•πr²/2d²

    B) U = E_o•Aπr²V²/2d

    Explanation:

    A) Since we have two circular plates, the formula for the electric field is expressed as;

    E = V/d

    Where;

    V is voltage

    d is distance

    However, the net electric field produced is given by;

    E’ = V/2d

    The tension in the cable can then be expressed as;

    F = qE’

    Where q is charge

    Thus;

    F = qV/2d – – – (eq 1)

    We also know that;

    C = q/V = E_o•A/d

    A is area = πr²

    Thus;

    q/V = E_o•πr²/d

    q = VE_o•πr²/d

    Let’s put VE_o•πr²/d for q in eq 1 to get;

    F = V²E_o•πr²/2d²

    B) formula for the energy stored in the electric field is;

    U = ½CV²

    From earlier, we saw that; C = E_o•A/d

    Thus;

    U = ½E_o•AV²/d

    A = πr²

    Thus;

    U = E_o•Aπr²V²/2d

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