UNIVERSITY OF SOUTHAMPTON PHYS1022W1

SEMESTER 1 EXAMINATION 2010/11

ELECTRICITY AND MAGNETISM

Duration: 120 MINS

VERY IMPORTANT NOTE

Section A answers MUST BE in a separate blue answer book. If any

blue answer booklets contain work for both Section A and B questions -

the latter set of answers WILL NOT BE MARKED.

Answer all questions in Section A and two and only two questions in

Section B.

Section A carries 1/3 of the total marks for the exam paper and you should

aim to spend about 40 mins on it. Section B carries 2/3 of the total marks for

the exam paper and you should aim to spend about 80 mins on it.

A Sheet of Physical Constants will be provided with this examination paper.

An outline marking scheme is shown in brackets to the right of each question.

Only university approved calculators may be used.

Copyright 2010 c© University of Southampton

Number of

Pages 9

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Section A

A1. In his famous 1909 experiment that demonstrated quantisation of electric

charge, R. A. Millikan suspended small oil drops in an electric field. With a

field strength of 20 MN/C, what mass drop can be suspended when the drop

carries a net charge of 10 elementary charges? [2]

A2. Suppose a disk with area A is placed in a uniform electric field of magnitude

E. The disk is oriented so that the vector normal to its surface, n, makes an

angle θ with the electric field. What is the electric flux through the surface of

the disk that is facing right in Figure 1? [2]

Figure 1: Question A2

A3. A conductor is placed in an external electrostatic field. The external field is

uniform before the conductor is placed within it. The conductor is completely

isolated from any source of current or charge.

(i) What is the net electric field inside the conductor?

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(ii) What is the charge density inside the conductor?

(iii) Assume that at some point just outside the surface of the conductor,

the electric field has magnitude E and is directed toward the surface of the

conductor. Give an expression for the charge density on the surface of the

conductor at that point. [4]

A4. In Figure 2 there are two point charges, +q and −q. There are also six

positions, labelled A through F, at various distances from the two point charges.

Draw a graph of potential along the horizontal line that runs through the two

charges, and rank the locations A to F on the basis of the electric potential at

each point. Rank positive electric potentials as larger than negative electric

potentials. [4]

Figure 2: Question A4

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A5. The same current I is flowing through two wires, labelled 1 and 2 in Figure 3, in

the directions indicated by the arrows. What is the direction of the net magnetic

field at each of the points labelled A, B and C? Indicate in a diagram the

directions of the components of the field at each point. [4]

Figure 3: Question A5

A6. Ampere’s law is given by:∮~B(~r) · d~l = µ0Iencl.

(i) Explain what the integral means, including the circle on the integral.

(ii) What physical property does the symbol Iencl represent?

(iii) Can Ampere’s law be used to find the magnetic field (a) around a long

straight current-carrying wire? (b) at the centre of a circular loop carrying a

constant current? Explain your answers. [4]

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Section B

B1. (a) A dipole lies on the axis and consists of an electron at y = 0.65 nm

and a proton at y = −0.65 nm.

(i) Find the electric field midway between the two charges.

(ii) Find the electric field at the point x = −1.5 nm , y = 0. [10]

(b) An isolated fixed metal sphere with diameter 4.0 cm carries a net

charge of 0.80 µC.

(i) What is the potential at the sphere’s surface?

(ii) If a proton were released from rest at the sphere’s surface, what

would be its speed far from the sphere? [10]

B2. (a) A thin rod of length L carrying charge Q distributed uniformly over its

length lies along the x-axis.

(i) What is the line charge density on the rod?

(ii) What must be the electric field direction on the rod’s perpendicular

bisector (taken to be the y-axis)?

(iii) Find an expression for the electric field at a point P a distance y

along the perpendicular bisector. The following standard integral can

be used:∫

dx/(x2 + a2)3/2 = [x/a2(x2 + a2)1/2] + constant [10]

(b) A long, thin wire carrying 6.2 nC/m runs down the centre of a long,

thin-walled, hollow pipe with radius 3.0 cm carrying -4.1 nC/m spread

uniformly over its surface. Find the electric field

(i) 1.5 cm from the wire, and

(ii) 4.5 cm from the wire. [10]

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B3. (a) A single-turn wire loop is 2.4 cm in diameter and carries a 630 mA

current.

(i) Find the magnetic field strength at the loop centre.

(ii) Find the magnetic field strength on the loop axis, 21 cm from the

centre. [10]

(b) In Figure 4 two point charges of magnitudes q1 and q2 are each

moving with speed v toward the origin (v << c). At the instant shown

q1 is at position (0, d) and q2 is at (d, 0).

(i) What is the magnitude of the electric force between the two

charges?

(ii) What is the magnitude of the magnetic force on q2 due to the

magnetic field caused by q1?

(iii) Assuming that the charges are moving nonrelativistically (v << c),

what can you say about the relationship between the magnitudes of

the magnetic and electrostatic forces? [10]

Figure 4: Question B3(b)

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B4. (a) In Figure 5, a conducting rod with length L = 33.0 cm moves in a

magnetic field ~B of magnitude 0.350 T directed into the plane of the

figure. The rod moves with speed v = 7.00 m/s in the direction shown.

(i) When the charges in the rod are in equilibrium, which point, a or b,

has an excess of positive charge?

(ii) In what direction does the electric field then point? Explain briefly.

(iii) When the charges in the rod are in equilibrium, what is the

magnitude E of the electric field within the rod?

(iv) Which point, a or b, is at higher potential? Explain your answer

using an expression that links electric field to potential.

(v) What is the magnitude Vba of the potential difference between the

ends of the rod?

(vi) What is the magnitude ε of the motional emf induced in the rod? [10]

Figure 5: Question B4(a)

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(b) A long solenoid has circular cross section of radius R. The solenoid

current is increasing with time, and as a result so is the magnetic field

in the solenoid. The field strength is given by B = bt, where b is a

constant, and t is time.

Find an expression for the magnitude of the electric-field strength

inside the solenoid a distance r from the axis. [5]

(c) Figure 6 shows a pair of parallel conducting rails a distance l apart

in a uniform magnetic field ~B. A resistance R is connected across

the rails, and a conducting bar of negligible resistance is being pulled

along the rails with velocity ~v to the right.

(i) What direction is the current in the circuit?

(ii) At what rate does the agent pulling the bar do work? [5]

Figure 6: Question B4(c)

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