11) A nonconducting sphere contains positive charge distributed uniformly throug

Question

11) A nonconducting sphere contains positive charge distributed uniformly throughout its volume. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.) A) The potential is highest at the center of the sphere B) The potential at the center of the sphere is zero C) The potential at the center of the sphere is the same as the potential at the surface D) The potential at the surface is higher than the potential at the center E) The potential at the center is the same as the potential at infinity Answer: A 12) A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the sphere's radius were twice as large, but the charge on the sphere were the same, what would be the potential on the surface relative to infinity? A) 50 V Answer: A 13) A conducting sphere 45 cm in diameter carries an excess of charge, and no other charges are present. You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. (k = 1/40-8998 109 N·m2/C2) The excess charge on this sphere is closest to A) 0.35 nC.B) 79 nC Answer: D 14) If the electric potential in a region is given by Vx) 6/x2, the x component of the electric field in that region is A) -12r-3 Answer: C 15) An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates All the geometric parameters of the capacitor (plate diameter and plate separation) are now DOUBLED. If the original capacitance was Co, what is the new capacitance? A) 4C0 Answer: B B) 25 V C) 100 V D) 200 V C) 315 nC. D) 350 nC. E) 700 nC. B) -6x C) 12r-3 D) 12r E) 6r B) 2C0 C) Co D) C0/2 16) Each plate of a parallel-plate air-filled capacitor has an area of 0.0020 m, and the separation of the plates is 0.020 mm. An electric field of 3.9 × 100 V/m s present between the plates. What is the surface charge density on the plates? (0-885 × 10-12 C2/N. m2) Answer: A 17) A charge of 2.00 flows onto the plates of a capacitor when it is connected to a 12.0-V potential source. What is the minimum amount of work that must be done in charging this capacitor? A)6.00 B)24.0 Answer C C) 12.0 HJ D) 144 uJ E) 576

Explanation / Answer

11)

The potential inside a charged, nonconducting sphere of radius R at a point r < R is given by:

E(r) = [k*Q/(2R)]*[3 - (r/R)^2]

where Q is the total charge on the sphere (assumed to be uniformly distributed), and k is the Coulomb constant.

At the center:

E(0) = 3k*Q/(2R)

At the surface (r = R)

E(R) = k*Q/R

Outside the sphere r > R), the potential is given by:

E(r) = k*Q/r (note that for r = R, this gives the same result as the previous one).

As r -> 8, E(r) -> 0

Answer: A) The potential is highest at the center of the sphere.

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