3. (a) Four point charges are placed at the vertices of a square as shown in the diagram.
The charges are of equal magnitude, Q, the sign of each charge is given in this diagram (attached).

(i) What is the value of V x E at all spatial points in this conﬁguration of charges (note that the charges are stationary)? What is the signiﬁcance of this result?

(ii) What is the electrostatic potential, V, at the following points: (0,0), (0, +a), (+a, 0)?

(iii) How much total work must be done to bring a charge of -2Q from spatial inﬁnity and place it at the origin?

(iv) With this ﬁfth point charge at the origin, how much total work must be done to place a sixth charge of +Q at the point (0, +a)?

(b) A dielectric slab (medium 2) is placed in the plane y = 0 and is surrounded by two other media as shown in
the adjacent diagram. The relative permittivities are (attached).

None of the media contain any free volume or surface charge. In medium 3 there is a uniform electric ﬁeld.

(i) State the boundary conditions on D and E at the interface between two materials.

(iii) Find the surface density of bound charge on both sides of the boundary between media 1 and 2, and on both sides of the boundary between media 2 and 3.

(iv) Does the magnitude of the electric ﬁeld vary from one medium to the next?
If so, in which medium is the magnitude of the electric ﬁeld the greatest?

Two particles with charges q1 and q2 are separated by distance d. Rank these scenarios according to the magnitude of the electrostatic (coulombic) potential energy. Ignore sign.
Scenario 1:
q1 = +4
q2 = -4
d = 4 A
Scenario 2:
q1 = +1
q2 = -1
d = 1 A
Scenario 3:
q1 = +1
q2 = -1
d = 3 A

Another illustration of the use of Legendre polynomials is provided by the problem of a neutral conducting sphere (radius r_0) placed in a (previously) uniform electric field (see attachment). The problem is to find the new, perturbed, electrostaticpotential. If we call the electrostaticpotential v, it satisfies [see the att

See the attached file.
1. The electrostatic field E in a particular region can be expressed in terms of spherical coordinates. Derive an expression for the potential difference.
2. The electrostaticpotential in a region is given by a function. Derive an expression for the electrostatic field in this region, and hence dete

Explain in everyday English and using formulas, the difference between 'electric potential' and 'electric potential energy'. Also explain, in the practical sense, why it matters that there is a difference. In other words, when will I ever see it? Also, explain why sometimes 'electrical' is interchanged with 'electrostatic' fo

If you remove all the electrons from a rain drop (diameter = 1 mm), what would be the
gain in the electrostaticpotential of the entire earth? Consider the radius of the
earth to be R=6378.14 km.
The answer clearly in by the simplest way illustrates the solution.

Compute the potential difference: change in V = V(5,2,1)-V(7,6,2) between the points (5,2,1) and (7,6,2) due to a constant electrostatic field given by E=(8i-7j+15k) N/C. Assume that all positions are measured in meters.

How do you show that the Green's function is always symmetric under Dirichlet boundary condition but symmetric under Neumann boundary condition only with certain modification? The specific problem is attached below.