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A)In a vacuum, the free...

A)In a vacuum, the free current density vector, J, and free voulme

charge density, P, are given by

J=v(epsilon not/meo not). Acos(x-ct)X

P=epsilon not.A cos(x-ct)

where A is a constant, and x,y and z are Cartesian coordinates and t is time.

(1) Write down Maxwell's equations.

(2)Find gradient.E.

(3) Show that E=Asin(x-ct)(x+z) is a possible solution for the

expression found in (2).

(4)Find delE/delt.

(5)Find gradient x E.

(6)Find delB/delt.

(7)Find gradient x B.

(8)Find a simple solution for B, assuming there are no steady magnetic fields in the region of space.

(9)Find gradient.B and explain what this result means physically.

B)

(1)Find an expression for the energy of a system of 4 charges (Q1,Q2.Q3,Q4) placed at the corners of a square of side a.

(2)Find the work needed to bring up a fifth charge,Q5, from infinity to the center of the square.

C)Two identical water drops are charged to the same potential, V0. Each carries a charge Q. The two drops coalesce to form one drop.

(1)Express the potential of the single drop in terms of V0.

(2)Find the charge in electrostatic energy in terms of V0 and Q.

charge density, P, are given by

J=v(epsilon not/meo not). Acos(x-ct)X

P=epsilon not.A cos(x-ct)

where A is a constant, and x,y and z are Cartesian coordinates and t is time.

(1) Write down Maxwell's equations.

(2)Find gradient.E.

(3) Show that E=Asin(x-ct)(x+z) is a possible solution for the

expression found in (2).

(4)Find delE/delt.

(5)Find gradient x E.

(6)Find delB/delt.

(7)Find gradient x B.

(8)Find a simple solution for B, assuming there are no steady magnetic fields in the region of space.

(9)Find gradient.B and explain what this result means physically.

B)

(1)Find an expression for the energy of a system of 4 charges (Q1,Q2.Q3,Q4) placed at the corners of a square of side a.

(2)Find the work needed to bring up a fifth charge,Q5, from infinity to the center of the square.

C)Two identical water drops are charged to the same potential, V0. Each carries a charge Q. The two drops coalesce to form one drop.

(1)Express the potential of the single drop in terms of V0.

(2)Find the charge in electrostatic energy in terms of V0 and Q.

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