electrostatics with two plane-parrallel electrodes

Given two plane-parallel electrodes, space d, at voltages 0 and V_0, find the currentdensity if an unlimited supply of electrons at rest is supplied to the lower potential electrode. Neglect collisions.

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Four point charges are located at the corners of a square in the xy plane. Their values and locations are as follows: q,(0,0); 2q,(0,a); 3q,(a,0); -4q,(a,a). Find E at the center of the square. See attachment.

A uniform infinite line charge is parallel to the z axis and intersects the xy plane at the point (a,b,0). Find the rectangular components of E produced at the point (0,c,0). See attachment for further details to the question.

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1. Two solid hemispherical conducting electrodes each of radius a are pressed into the earth, curved surfaces down, such that the flat surfaces are flush with the flat surface of the earth. Assume that the electrode separation (center to center) is d where d>>a. We wish to measure the electric

4a. Consider the parallel plate capacitor, where the surface charge density is 0.02 uC/m^2, and the distance between the plate is 0.01m. What is the potential difference between the two plates?
4b. What would be the change in potential energy of the electron as it moves from the negative plate to the positive plate?
4c.

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1. Consider two infinite parallel plane conducting plates, of finite thickness, with separation d. Suppose a charge density of sigma; is placed on one plate, while the other plate has -2sigma.
A) Determine the resulting charge densities on each of the 4 surfaces
B) De

1. Find the intersection point of the line (x-1)/2=(y+1)/3=z-2 and the plane 2x+y-z=17.
2. Find the distance from point Q(1,-2,3) to the plane 2x-y-z=6.
Need steps and solutions.....Thanks!

Two point charges lie along the y axis. A charge of q1 = -11 micro Coulombs is at y=8.0m and a charge of q2 =-4.0 micro Coulombs is at the y=-1.0m. Locate the point (other than infinity) at which the total electric field is zero.

1 Given a = 9i - 5j and b = 7i-4j, express i and j in terms of a and b
2 Given a=<4,5,-3> and b =<4,-2,2> determine whether a and b are parrallel, perpendicular, or neither.
3 Given F = 4i -2k;..... P(0,1,0) and Q(4,0,1) find the work W done by the force (F)moving a particle in a straight line from P to Q.
4 Given a