PhysicsLAB AP Free Response Question
2006 C3 E&M

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A loop of wire of width w and height h contains a switch and a battery and is connected to a spring of force constant k, as shown below.
The loop carries a current I in a clockwise direction, and its bottom is in a constant, uniform magnetic field directed into the plane of the page.
(a) On the diagram of the loop below, indicate the directions of the magnetic forces, if any, that act on each side of the loop.

 (b) The switch S is opened, and the loop eventually comes to rest at a new equilibrium position that is a distance x from its former position. Derive an expression for the magnitude of the uniform magnetic field in terms of the given quantities and fundamental constants.

The spring and loop are replaced with a loop of the same dimensions and resistance R but without the battery and switch. The new 1oop is pulled upward, out of the magnetic field, at constant speed v . Express algebraic answers to the following questions in terms of Bo , vo , R, and the dimensions of the loop.
(c) i. On the diagram of the new loop below, indicate the direction of the induced current in the 1oop as the loop moves upward.

 (c) ii. Derive an expression for the magnitude of this current.

 (d) Derive an expression for the power dissipated in the loop as the loop is pulled at constant speed out of the field.

 (e) Suppose the magnitude of the magnetic field is increased. Does the external force required to pull the loop at speed v increase, decrease, or remain the same? Justify your answer.

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