Chapter 2: Q10P (page 70)
A charge q sits at the back comer of a cube, as shown in Fig. 2.17.What is the flux of E through the shaded side?
Short Answer
The electric flux through the shade area is.
Chapter 2: Q10P (page 70)
A charge q sits at the back comer of a cube, as shown in Fig. 2.17.What is the flux of E through the shaded side?
The electric flux through the shade area is.
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Get started for freeFind the net force that the southern hemisphere of a uniformly charged solid sphere exerts on the northern hemisphere. Express your answer in terms of the radius R and the total charge Q.
A sphere of radius Rcarries a charge density (where kis a constant). Find the energy of the configuration. Check your answer by calculating it in at least two different ways.
Find the electric field at a height zabove the center of a square sheet (side a) carrying a uniform surface charge .Check your result for the limitingcases and z >> a.
In a vacuum diode, electrons are "boiled" off a hot cathode, at potential zero, and accelerated across a gap to the anode, which is held at positive potential . The cloud of moving electrons within the gap (called space charge) quickly builds up to the point where it reduces the field at the surface of the cathode to zero. From then on, a steady current flows between the plates.
Suppose the plates are large relative to the separation (in Fig. 2.55), so
that edge effects can be neglected. Thenlocalid="1657521889714" and (the speed of the electrons) are all functions of x alone.
(a) Write Poisson's equation for the region between the plates.
(b) Assuming the electrons start from rest at the cathode, what is their speed at point x, where the potential is
(c) In the steady state,localid="1657522496305" is independent of . What, then, is the relation between p and v?
(d) Use these three results to obtain a differential equation for, by eliminatingand.
(e) Solve this equation for as a function of ,and . Plot , and compare it to the potential without space-charge. Also, findandas functions of .
(f) Show that
and find the constant. (Equation 2.56 is called the Child-Langmuir law. It holds for other geometries as well, whenever space-charge limits the current. Notice that the space-charge limited diode is nonlinear-it does not obey Ohm's law.)
An inverted hemispherical bowl of radius Rcarries a uniform surface charge density .Find the potential difference between the "north pole" and the center.
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