Exam1_2008Spring_Solutions

Exam1_2008Spring_Solutions - MASSACHUSETTS INSTITUTE OF...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2008 8.02 Exam One Solutions Spring 2008 SECTION I In this section you are asked to answer 5 questions, each worth 5 points. You do not have to show your work; in most cases you may simply circle the chosen answer. Question 1 (5 points): Consider the hollow conductor shown in the figure which has zero net charge. As shown, an object with charge Q + is placed inside the neutral, hollow, spherical conductor. Indicate the direction of the electric field that arises after static equilibrium has been achieved by sketching several representative field lines everywhere in space as needed. +Q
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2 Question 2 (5 points): Consider the two charges 2 Q + and Q , and a mathematical spherical surface (it does not physically exist) as shown in the figure below. The electric flux on the spherical surface between the charges is… a) positive. b) negative. c) zero. d) undetermined by the information given. Solution: c). Only the charge enclosed in a surface contributes to the electric flux on that surface. Both charges do contribute to the electric field. However if a charge is outside a closed surface then the electric flux on that surface due only to that charge is zero. Since both charges lie outside the surface, the electric flux on the surface due to those two charges is zero.
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3 Question 3 (5 points): A positive charge Q + is moved by an external agent from infinity to a point midway between two charges 3 q + and - q that are separated by a distance d . The positive charge Q + begins and ends at rest. The work done by the external agent is a) zero. b) e kqQ d + . c) e d . d) 2 e d + . e) 2 e d . f) 3 e d + . g) 3 e d . h) 4 e d + . i) 4 e d . j) none of the above. Solution: h). The work done by the external agent is equal to the change in electric potential energy which is given by the charge Q + times the electric potential difference between infinity and the point between the charges: 34 (() () ) /2 ee e ext kq WQ V P V Q dd d ⎛⎞ =+ ∞ =+ ⎜⎟ ⎝⎠
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4 Question 4 (5 points): The circle is at +5 V relative to the plate. Which of the below are the most accurate contours for the equipotentials ( equipotential map) ? Solution d). The strongest electric field is in the region between the circle and the plate and so the gradient of the electric potential is largest there. Thus we should have more contours in that region. Figure e) is the correct figure for the electric field lines. We can rule out answer b), because equal spaced contours above and below the circle at 5V implies that the electric field is radially symmetric but it must curve down to the plate as shown in e) in order to be perpendicular to the conductor. The contours in f) imply the electric field is strongest above the circle which is not correct.
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This note was uploaded on 10/22/2008 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.

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Exam1_2008Spring_Solutions - MASSACHUSETTS INSTITUTE OF...

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