Electricity and Magnetism Answers

Two flat mirrors are perpendicular to each other. An incoming beam of light makes an angle of 15° with the first mirror as shown below. What angle will the outgoing beam make with the surface of the second mirror?

(a) What is the wavelength (in meters) of a 93.3 MHz Radio wave frequency? (b) What is the frequency (in Hz) of an x-ray beam with wavelength of 0.0100 nm?

Two positive charges are separated by a distance R. If the distance between the charges is reduced to R/2, what happens to the total electric potential energy of the system

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 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

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)?

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

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

(b) x^2 y = 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

Point charges Q1 =1 nC and Q2 = 2 nC are at a distance apart. Which of the following statements are incorrect?

(a) The force on Q1 is repulsive.

(b) The force on Q2 is the same in magnitude as that on Q1.

(c) As the distance between them decreases, the force on Q1 increases linearly.

(d) The force on Q2 is along the line joining them.

(e) A point charge Q3 = -3 nC located at the midpoint between Q1 and Q2 experiences no net force.

The electric flux density on a spherical surface r = b is the same for a point charge Q located at the origin and for charge Q uniformly distributed on surface r = a(a < b).

(a) Yes

(b) Not necessarily

(c) No

An electric potential field is produced by point charges 1 mC and 4 mC located at (-2, 1, 5) and (1, 3, -1), respectively. The energy stored in the field is