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Problem Set 7

# Problem Set 7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2008 Problem Set 7 Due: Wednesday, April 2 at 11 am. Hand in your problem set in your section slot in the boxes outside the door of 32- 082. Make sure you clearly write your name, section, table, group (e.g. L01 Table 3 Group A) Problem 1: (a) Force on the Rectangular Loop (5 points) In the figure on the right, the current in the long, straight wire is I 1 and the wire lies in the plane of the rectangular loop of length A and width a , that carries the current I 2 . The distance between the left side of the rectangular loop and the straight wire is c . Find the magnitude and direction of the net force exerted on the loop by the magnetic field created by the wire. (b) Levitating Wire (5 points) A copper wire of diameter d carries a current density J G at the earth’s equator where the earth’s magnetic field is horizontal, points north, and has magnitude -4 0.5 10 T earth = × B G . The wire lies in a plane that is parallel to the surface of the earth and is oriented in the east-west direction. The density of copper is 3 -3 8.9 10 kg m Cu ρ = × . The resistivity of copper is 8 1.7 10 m r ρ = × . a) How large must J G be, and which direction must it flow in order to levitate the wire? Use -2 9.8m s g = b) When the wire is floating how much power will be dissipated per cubic centimeter?

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Problem 2: Particle Orbits in a Magnetic Field The entire x-y plane to the right of the origin O is filled with a uniform magnetic field B pointing out of the page, as shown. Two charged particles travel along the negative x axis in the positive x direction, each with speed V, and enter the magnetic field at the origin O. The two particles have the same charge mass m , but have different charges, q 1 and q 2 . When in the magnetic field, their trajectories both curve in the same direction (see sketch), but describe semi-circles with different radii. The radius of the semi-circle traced out by particle 2 is exactly twice as big as the radius of the semi-circle traced out by particle 1. (a) Are the charges of these particles positive or negative? (b) Derive (do not simply state) an expression for the radius R 1 of the semi-circle traced out by particle 1, in terms of q 1 , V , B , and m . (c) What is the ratio q 2 /q 1 ? (d) Is it possible to apply an electric field E in the region x > 0 only which will cause both particles to continue to move in a straight line after they enter the region x > 0 ? If so, indicate the magnitude and direction of that electric field, in terms of the quantities given. If not, why not?
Problem 3: Triangular Loop A current loop, carrying a current I shown in the figure on the right, is in the shape of a right triangle with sides 40 cm a = , 30 cm b = , and hypotenuse of length 50 cm. The loop is in a uniform magnetic field B whose direction is parallel to the current in the 30 cm side of the loop (pointing up in the figure).

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Problem Set 7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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