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Show that the D field due to a point charge has a divergence of zero
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- Repeat the previous problem, assuming that the electric field is directed along a body diagonal of the cube.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?Calculate the electric field due to a uniformly charged rod of length L, aligned with the x-axis with one end at the origin; at a point P on the z-axis.
- 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.)Charge 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.Find the electnc field intensity at the point P(8,4,4) due to a uniform line charge lying along the x-axis and extending from (6) to + (-6)?
- Find the electric field a distance z above the midpoint of a straight line segment of length 2L, which carries a uniform line charge A.Three identical infinite uniform line charges of (5 μC/m) lie along the (positive and negative) x, y and z axes in free space. Find E at: PA(0, 0, 3) due to line charge of x-axes?Find the electric field of a distance z above the midpoint of a straight line segment of length 2 L, which carries a uniform line charge A.
- Prove that electrostatic force is a conservative force for any configuration of charges.Find the electric field a distance z above the center of a circular loop of radius r (See attatched figure) that carries a uniform line charge λ.Consider a uniformly charged, thin-walled, right circular cylindrical shell having total charge Q, radius R, and length l. Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Find the field it creates at the same point.