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fall_03_exam1_sol_phy2054 - Solution to Exam 1 Paul Avery...

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Solution to Exam 1 Paul Avery, Arthur Hebard PHY2049, Fall 2003 Sep. 24, 2003 1. Two parallel conducting plates are brought to a potential difference of 4000 V and a small object of mass 4 mg and charge 0.2 µ C accelerates from rest at one plate. With what speed in m/s will it reach the other plate? Solution: The work done by the electric field is qV , where q is the charge and V is the potential difference. Thus the kinetic energy is K = qV . Solving 1 2 mv 2 = qV for the velocity v gives v = 2 qV/m , yielding v = 20m/s. 2. Consider a dipole with dipole moment p oriented at an angle θ with respect to a constant electric field E . At what angle θ in degrees is the torque τ a maximum, and what is the magnitude of τ for this orientation? Solution: The torque is maximum when the dipole is oriented perpendicular to the electric field. Thus θ = 90 and τ = pE . 3. Five capacitors, each of capacitance C , are connected as shown in the figure. What is the equivalent capacitance of the arrangement? Solution: It’s best to do this in stages. Capacitors add in parallel, so the arrangement can be immediately simplified to 2 C , C and 2 C in series. The equivalent capacitance can be found from C eq = 1 / 2 C + 1 /C + 1 / 2 C , giving C eq = C/ 2.
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