Electricity and Magnetism Answers

A microscope is sharply focused on a mark. When a parallel plate of glass 4.8 mm thick is placed over the mark, the microscope has to be raised 0.18 cm to refocus. What is the refractive index of the glass?

A charge Q is uniformly distributed throughout a sphere of radius a. Taking the potential at infinity as zero, the potential at r = b < a is

A potential field is given by V = 3x^2y - yz. Which of the following is not true?

(a) At point (1, 0, -1) V and E vanish.

(b) x^2y = 1 is an equipotential line on the xy-plane.

(c) The equipotential surface V = - 8 passes through point P + 2, -1, 4)

(d) The electric field at P is 12ax - 8ay - az V/m.

(e) A unit normal to the equipotential surface V = - 8 at P is -0,83ax + 0,55ay+ 0,07az.

The work done by the force F = 4ax - 3ay + 2az N in giving a 1 nC charge a displacement of 10ax + 2ay - 7az m is

Point charges 30 nC, - 20 nC, and 10 nC are located at (-1, 0, 2), (0, 0, 0) and (1, 5, -1) respectively. The total flux leaving a cube of side 6 m centered at the origin is

Suppose a uniform electric field exists in the room in which you are working, such that the lines of force are horizontal and at right angles to one wall. As you walk toward the wall from which the lines of force emerge into the room, are you walking toward

(a) points of higher potential?

(b) points of lower potential?

(c) points of the same potential (equipotential line)?

 The electric potential in some region in space is given by V (r) = C/r where r = p x 2 + y 2 + z 2 and C is a positive constant. (a) calculate an expression for the electric field in this region. (b) note that ~r = xˆi + ˆj + z ˆk and ~r = rrˆ, express E~ in spherical coordinates. Here ˆr is the radial unit vector of spherical coordinates, sometimes denoted as ˆer. (c) Look and report the expression for the gradient operator in spherical coordinates. Re-derive the expression for E~ , now directly in spherical coordinates.

(a)Derive an expression for VA − VB, the potential difference between points A and B (b) Does your result reduce to the expected answer when d = 0? When a = 0? and when q = 0.