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The figure below shows three wire loops, arranged as shown so that their upper edges are aligned. The loop all have the same clockwise current i = .5A flowing around them and all have edge lengths of either L = 0.14m or L/2 = 0.07m. i a b

The figure below shows three wire loops, arranged as shown so that their upper edges are aligned. The loop all have the same clockwise current i = .5A flowing around them and all have edge lengths of either L = 0.14m or L/2 = 0.07m. i a b

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(e) FOR E LEVEL WORK: Write a convincing argument for the general result that the net magnetic force is zero on any closed loop of current in a uniform magnetic field. Discuss the direction of the net force on a loop of current in a nonuniform field in terms of the direction of the dipole moment and the gradient of the field (the direction in which the field strength is decreasing.) Diagrams illustrating this will be very helpful both in developing your understanding and communicating it.
Transcribed Image Text:(e) FOR E LEVEL WORK: Write a convincing argument for the general result that the net magnetic force is zero on any closed loop of current in a uniform magnetic field. Discuss the direction of the net force on a loop of current in a nonuniform field in terms of the direction of the dipole moment and the gradient of the field (the direction in which the field strength is decreasing.) Diagrams illustrating this will be very helpful both in developing your understanding and communicating it.
Problem 5 The figure below shows three wire loops, arranged as shown so that their upper edges are aligned. The loop all have the same clockwise current i = .5A flowing around them and all have edge lengths of either L = 0.14m or L/2 = 0.07m. i b A magnetic field, B, points into the page everywhere. The magnitude of the field does not vary as we move horizontally across the page but DOES vary as you move vertically, up and down the page. The field is strongest at the top of the loops, and decreases linearly to its weakest (smallest magnitude) at the bottom of loop a. Please note that the DIRECTION of the field is always into the page - it is the variation in magnitude that depends on the vertical location of the test point. (a) What is the direction of the magnetic force on each segment of each loop due to the field? Draw a diagram of the loops and these forces. (b) We would like to analyze the net magnetic force on each loop, which is the sum of the forces on each of the four edges of the loop. Do any of these forces cancel? If so, which ones? (c) Rank the loops according to the magnitude of this net force, greatest first. Use conceptual arguments rather than calculations. (d) Find a general expression (in terms of iL, L and the field values at the top and bottom, B and Bu respectively) for the net force on loop a (square, sides length L.) Compare to your earlier conceptual ranking to check your work.
Transcribed Image Text:Problem 5 The figure below shows three wire loops, arranged as shown so that their upper edges are aligned. The loop all have the same clockwise current i = .5A flowing around them and all have edge lengths of either L = 0.14m or L/2 = 0.07m. i b A magnetic field, B, points into the page everywhere. The magnitude of the field does not vary as we move horizontally across the page but DOES vary as you move vertically, up and down the page. The field is strongest at the top of the loops, and decreases linearly to its weakest (smallest magnitude) at the bottom of loop a. Please note that the DIRECTION of the field is always into the page - it is the variation in magnitude that depends on the vertical location of the test point. (a) What is the direction of the magnetic force on each segment of each loop due to the field? Draw a diagram of the loops and these forces. (b) We would like to analyze the net magnetic force on each loop, which is the sum of the forces on each of the four edges of the loop. Do any of these forces cancel? If so, which ones? (c) Rank the loops according to the magnitude of this net force, greatest first. Use conceptual arguments rather than calculations. (d) Find a general expression (in terms of iL, L and the field values at the top and bottom, B and Bu respectively) for the net force on loop a (square, sides length L.) Compare to your earlier conceptual ranking to check your work.
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