Download Section B - University of Southampton

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.
Number of
c University of Southampton
Copyright 2010 °
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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
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carries a net charge of 10 elementary charges?
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, n̂, makes an
angle θ with the electric field. What is the electric flux through the surface of
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the disk that is facing right in Figure 1?
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
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conductor at that point.
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
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potentials.
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
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directions of the components of the field at each point.
Figure 3: Question A5
A6. Ampère’s law is given by:
H
~ r) · d~l = µ0 Iencl .
B(~
(i) Explain what the integral means, including the circle on the integral.
(ii) What physical property does the symbol Iencl represent?
(iii) Can Ampère’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
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constant current? Explain your answers.
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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.
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(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?
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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:
R
dx/(x2 + a2 )3/2 = [x/a2 (x2 + a2 )1/2 ] + constant
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(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.
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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
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centre.
(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
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the magnetic and electrostatic forces?
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
~ of magnitude 0.350 T directed into the plane of the
magnetic field B
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?
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.
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(c) Figure 6 shows a pair of parallel conducting rails a distance l apart
~ . A resistance R is connected across
in a uniform magnetic field B
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?
Figure 6: Question B4(c)
END OF PAPER
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