Practice Final

Problem 3 part d s q0 q0 r k5 q0 r q0 the capacitor

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Unformatted text preview: charge from r=3R to r=2R? Problem 3 Part (d) S Q0 Q0 R K=5 -Q0 R -Q0 The capacitor in the figure has C=1F and is initially charged with Q0=1C. The resistor has R=100Ω. At t=0 the switch S is closed. (a) Find the current through R immediately after the switch is closed, I(t=0+), in A. (b) Find the energy dissipated in the resistor during the first second after the switch is closed, in J, accurate to 5 decimal places at least. Compare your answer with [I(t=0+)]2Rx1s, and explain why it is similar or very different. (c) Find the total energy dissipated in the resistor after a long time has passed, in J. (d) Suppose before you close S you insert between the plates of the capacitor a dielectric of dielectric constant K=5. Find the answer for point (c) again. (e) If the answers to (c) and (d) were different, explain how to account for the difference in energy. Where did the extra energy go, or where did the extra energy come from? ! Problem 4 The electric field in a region of space that extends 2m from the origin in all directions is given by r yˆ xˆ E ( x, y, z) = ( i " j )V / m with x0=y0=1m. y0 x0 (a) Explain why this cannot be an electrostatic field (i.e. a field that is produced by static electric charges). (b) Assuming the magnetic field at point (0,0,0) is 0 at time t=0, find its magnitude at time t=1s, in T. (c) A square loop of wire of resistance R=2Ω lies on the xy plane with vertices at points (0,0), (1m,0), (1m,1m), (0,1m). Find the current that circulates through that loop, in A. (d) Looked at from a point on the +z axis, does the current flow clockwise or counterclockwise? Problem 5 Slanted view picture loop 1 loop 2 I Side view picture loop1 v x axis loop 2 Circular loops 1 and 2 are on a plane perpendicular to the paper (side view picture). Loop 1 moves at uniform speed v along a line (dashed line) (x axis) that goes over loop 2 very close to it , such that the center of loop 1 flies right ove...
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