0222_E3_Q - Y(c The gap between plates X and Y is then...

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PHY 0222 STOT Problem Set E3 (March 17, 2010) 1. A conical surface (empty ice-cream cone) carries a uniform surface charge density σ . The height of the cone and the radius at the top are both equal to a (Fig. 1). Find the potential difference between the vertex P and the centre of the top Q . [ Hint: The conical surface can be divided into many differential rings, each of area 4 cos 2 π dz z × . Do you know why? The following integral may be useful: () ( ) 1 2 ln 2 0 2 2 + = + a a z a z zdz ] Fig. 1 z 2. Three conducting plates X , Y , Z , each of area A , are placed parallel to each another and separated by gaps d 1 and d 2 (Fig. 1). Plate Y carries a total charge of + q . Plates X and Z , which carry a total charge of – q , are connected by a wire. (a) Find the ratio of the electric fields in the gaps. (b) What are the charges, 1 q and 2 q , residing on the upper and lower surfaces of the plate
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Unformatted text preview: Y ? (c) The gap between plates X and Y is then filled completely with a material of resistivity η , so that a current I flows from Y to X with a uniform current density. Draw an equivalent RC circuit for the system, and hence find the initial current and the time for the current to drop to 1 − e of the initial value (Neglect dielectric effect). Fig. 1 3. A non-conducting circular disc of radius R has a total charge +q uniformly distributed over its surface. The disc rotates about its axis at a constant angular velocity ω . Starting from Biot-Savart law, derive an expression for the magnetic field produced by the disc along its axis. In particular, what is the magnetic field at the centre of the disc? [ Hint : ( ) z z R z R dr z r r R 2 2 2 2 2 2 2 3 2 2 3 − + + = + ∫ ]...
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