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- A total charge Q is distributed uniformly throughout a spherical volume that is centered at o1 and has a radius R. Without disturbing the charge remaining charge is removed from the spherical volume that is centered at o2 (see below). Show that the electric field everywhere in the empty region is given by E=Qr40R3 where r is the displacement vector directed from o1 to o2 .The charge per unit length on the thin rod shown below is . What is the electric field at the point P? (Hint: Solve this problem by first considering the electric field dE at P due to a small segment dx of the rod, which contains charge dq=dx . Then find the net field by integrating dE over the length of the rod.)Two non-conducting spheres of radii R1 and R2 are uniformly charged with charge densities p1 and p2 , respectively. They are separated at center-to-center distance a (see below). Find the electric field at point P located at a distance r from the center of sphere 1 and is in the direction from the line joining the two spheres assuming their charge densities are not affected by the presence of the other sphere. (Hint: Work one sphere at a time and use the superposition principle.)
- Shown below ale two concentric conducting spherical shells of radii R1 and R2 , each of finite thickness much less than either radius. The inner and outer shell carry net charges q1 and q2 , respectively, where both q1 and q2 are positive. What is the electric field for (a) rR1 ; (b) R1rR2 , and (c) rR2 ? (d) What is the net charge on the inner surface of the inner shell, the outer surface of the inner shell, the inner surface of the outer shell, and the outer surface of the outer shell?The infinite slab between the planes defined by z=a/2 and z=a/2 contains a uniform volume charge density p (see below). What is the electric field produced by this charge distribution, both inside and outside the distribution?A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges +Q and Q , respectively. Assuming that the length L of both conductors is much greater than a or b, determine the electric field as a function of r, the distance from the common central axis of the cylinders, for (a) ra; (b) arb; and (c) rb.
- The conductor in the preceding figure has an excess charge of 5.0C . If a 2.0C point charge is placed in the cavity, what is the net charge on the surface of the cavity and on the outer surface of the conductor?The electric field in a region is given by E=al(b+cx)i, where a=200 N ? m/C, b=2.0 m, and c=2.0 . What is the net charge enclosed by the shaded volume shown below?Two large copper plates facing each other have charge densities 4.0C/m2 on the surface facing the other plate, and zero in between the plates. Find the electric flux through a 3cm4cm rectangular area between the plates, as shown below, for the following orientations of the area. (a) If the area is parallel to the plates, and (b) if the area is tilted =30 from the parallel direction. Note, this angle can also be =180+30.
- Charge is distributed uniformly with a density p throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that E=pr20 (rR); E=pR220r (rR).Point charges q1=50C and q2=25C are placed 1.0 m apart. (a) What is the electric field at a point midway between them? (b) What is the force on a charge q3=20C situated there?A particle of charge q and mass m is placed at the center of a uniformly charged ring of total charge Q and radius R. The particle is displaced a small distance along the axis perpendicular to the plane of the ring and released. Assuming that the particle is constrained to move along the axis, show that the particle oscillates in simple harmonic motion with a frequency f=12qQ40mR3.