2. A spherical capacitor consists of an inner solid conducting sphere of radius a surrounded by a spherical conducting shell of inner radius b and outer radius e. The capacitor is charged with –Q on the inner sphere and +Q on the outer spherical shell. a) Derive expressions for the electric field everywhere in space due to this charge configuration, indicating both direction and magnitude, in terms of the distance r from the center. Graph the electric field magnitude as a function of r. b) What is the surface charge density on the outer surface of the inner sphere and on the inner surface of the outer sphere? c) In part d) you will calculate the potential difference AV between the inner and outer conductors. Before you calculate the value, indicate what the sign (positive or negative) of AV=Vb – Va must be and give a clear explanation as to why.

A solid disk of radius R = 11 cm lies in the y-z plane with the center at the origin. The disk carries a uniformly distributed total charge Q = 45 μC. A point P is located on the positive half of the x-axis a distance 24 cm from the origin. Refer to the diagram, where the y- and z-axes lie in the plane of the screen and the x-axis points out of the screen. a. Enter an expression for the surface charge density σ in terms of the total charge and radius of the disk. σ = b. Consider a thin ring of the disk of width dr located a distance r from the center. Enter an equation for the infinitesimal charge in this thin ring in terms of Q, R, r, and dr. dQ = c.  Calculate the electric potential at P, in kilovolts. V = d.  Calculate the magnitude of the electric field at the point P in units of meganewtons per coulomb. E =

1. a nonconducting rod of length L has charge -q uniformly distributed along its length. (a) What is the linear charge density of the rod? (b) What is the electric field at point P, a distance a from the end of the rod? (c) If P were very far from the rod compared to L, the rod would look like a point charge. Show that your answer to (b) reduces to the electric field of a point charge for a >> L.

A Van de Graaff generator has a 0.045 mC charge on its conducting spherical terminal. a.What is the magnitude of the electric field 2.7 m from the center of the terminal of the Van de Graaff generator? Since that distance is greater than the radius of the terminal, the field is the same as that due to the same charge concentrated at the center. Give your answer in newtons per coulomb.  b. At this distance, what is the magnitude of the force that the field exerts on a 2.1 μC point charge on the Van de Graaff generator's belt? Give your answer in newtons.

ST At a distance of 48.7 cm from a very long (essentially infinite) uniform line of charge, the electric field strength is 1,866 N/C. At what distance (in cm) from the line will the field strength be equal to 811 N/C? X

esc The nucleus of a 125 Xe atom (an isotope of the element xenon with mass 125 u) is 6.0 fm in diameter. It has 54 protons and charge q = +54e. R 2 R F2 W # 3 80 E $ 4 R Part A What is the electric force on a proton 2.6 fm from the surface of the nucleus? Hint: Treat the spherical nucleus as a point charge. Express your answer with the appropriate units. F= 8.64 Part B μà 1 Submit Previous Answers Request Answer % 5 X Incorrect; Try Again; 4 attempts remaining F5 What is the proton's acceleration? Express your answer with the appropriate units. Value T → HA N 6 C FIC ? Units MacBook Air Y & 7 U * 8 FB ( 9 F9 0 0 P + Review

4. A point charge q=+15.0µC is located at the origin. A hollow spherical conductor of inner radius a=0.0500 m and outer radius b=0.0950 m is concentric with the point charge, and has a net charge Q= -20.0µC. Using Gauss's law, derive the equation for the magnitude of the electric field as a function of r. a

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I Review A positive point charge q sits at the center of a hollow spherical shell. The shell, with radius R and negligible thickness, has net charge -2q. Part A Find an expression for the electric field strength inside the sphere, r R. Give your answer as a multiple of q/e0. ? Submit Request Answer 圓