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- Discuss the restrictions on the Gaussian surface used to discuss planar symmetry. For example, is its length important? Does the cross-section have to be square? Must the end faces be on opposite sides of the sheet?Check Your Understanding How will the System above change if there are charged objects external to the sphere?Repeat the preceding problem, with E=2xi+3x2k.
- Find the electric field at P for the charge configurations shown below.Repeat your calculations for the preceding problem, given that the charge is distributed uniformly over the surface of a spherical conductor of radius 10.0 cm.Consider a point charge 3Q is located at the origin. Divergence of the electric fluxdensity produced by the charge is
- An electron is at rest just above the surfaceof a sphere with a radius of 2.7 mm and a uniformly distributedpositive charge of 1.8 * 10-15 C. Like a rocket blasting off fromthe Earth, the electron is given an initial speed ve radially outwardfrom the sphere. If the electron coasts to infinity, where its kineticenergy drops to zero, what is the escape speed, ve?An ideal uniformly charged ring is situated on the xy-plane withits center at the origin. Assuming that the charge of the ring is negative,a proton moving in the +z -axis going to the origin willCharge is distributed uniformly with a density ρ throughout an infinitely long cylindrical volume ofradius R. Show that the field of this charge distribution is directed radially with respect to the cylinder.
- 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.)Check Your Understanding Check that the electric fields for the sphere reduce to the correct values for a point charge.Can you arrange the two point charges q1=2.0106C and q2=4.0106C along the x-axis so that E=0 at the origin?