2011年AP电磁学简答题真题+答案+PDF下载
E&M. 1.
A nonconducting, thin, spherical shell has a uniform surface charge density s on its outside surface and no charge anywhere else inside.
(a) Use Gauss’s law to prove that the electric field inside the shell is zero everywhere. Describe the Gaussian surface that you use.
(b) The charges are now redistributed so that the surface charge density is no longer uniform. Is the electric field still zero everywhere inside the shell?
____ Yes ____ No ____ It cannot be determined from the information given.
Justify your answer.
Now consider a small conducting sphere with charge +Q whose center is at corner A of a cubical surface, as shown below.
(c) For which faces of the surface, if any, is the electric flux through that face equal to zero?
____ ABCD ____ CDEF ____ EFGH ____ ABGH ____ BCFG ____ ADEH
Explain your reasoning.
(d) At which corner(s) of the surface does the electric field have the least magnitude?
(e) Determine the electric field strength at the position(s) you have indicated in part (d) in terms of Q, L, and fundamental constants, as appropriate.
(f) Given that one-eighth of the sphere at point A is inside the surface, calculate the electric flux through face CDEF.
E&M. 2.
The circuit represented above contains a 9.0 V battery, a 25 mF capacitor, a 5.0 H inductor, a 500Ω resistor,and a switch with two positions, S1 and S2 . Initially the capacitor is uncharged and the switch is open.
(a) In experiment 1 the switch is closed to position S1 at time t1 and left there for a long time.
i. Calculate the value of the charge on the bottom plate of the capacitor a long time after the switch is closed.
ii. On the axes below, sketch a graph of the magnitude of the charge on the bottom plate of the capacitor as a function of time. On the axes, explicitly label any intercepts, asymptotes, maxima, or minima with numerical values or algebraic expressions, as appropriate.
iii. On the axes below, sketch a graph of the current through the resistor as a function of time. On the axes, explicitly label any intercepts, asymptotes, maxima, or minima with numerical values or algebraic expressions, as appropriate.
(b) In experiment 2 the capacitor is again uncharged when the switch is closed to position S1 at time t1 . The switch is then moved to position S2 at time t2 when the magnitude of the charge on the capacitor plate is 105 mC,allowing electromagnetic oscillations in the LC circuit.
i. Calculate the energy stored in the capacitor at time t2 .
ii. Calculate the maximum current that will be present during the oscillations.
iii. Calculate the time rate of change of the current when the charge on the capacitor plate is 50 mC.
2011年AP电磁学简答题真题余下省略！
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