l icisplere. Express your answer in terms of the radius R and the total charge Q
ID: 3281371 • Letter: L
Question
l icisplere. Express your answer in terms of the radius R and the total charge Q. [Answer: (1 /4 )(3Q2/16R2)] Problem 2.59 Prove or disprove (with a counterexample) the following Theorem: Suppose a conductor carrying a net charge Q. when placed in an external electric field E, experiences a force F: if the external field is now reversed (E, -Ee), the force also reverses (F -F). What if we stipulate that the external field is uniform? Problem 2.60 A point charge g is at the center of an uncharged spherical conducting shell, of inner radius a and outer radius b. Question: How much work would it take to move the charge out to infinity (through a tiny hole drilled in the shell)? [Answer: Problem #8 (not from! Griffiths!). Two metal spheres, ofradi R1 andR|are far apart from one another compared with these radii. Given a total amount of charge Q, how should it be divided so as to make the potential energy of the system as small as possible? Show that with that division the potential difference between the two spheres is zero. Problem #9 (not from Griffiths). Consider a capacitor made of four parallel plates with large area A, evenly spaced with small separation s. The first and 2 2 as are the second and fourth. What is the capacitance of this system?Explanation / Answer
When a conductor is placed in an electric field, charges will be induced on the surface of conductor such that net field inside the conductor is zero. Since the conductor is already carrying some charge, this will also be on the surface of conductor. These charges experience external non-uniform electric field. Hence net force on the conductor is not zero.
When the direction of field is reversed everywhere, sign of the induced charge also gets reversed. Hence force is still in the same direction as before.
Hence the above statement is not true.
If the field is uniform, then the net force on conductor is zero. Hence the statement will be true.
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