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A 2.00 -m length of wire is held in an east-west direction and moves horizontally to the north with a speed of 15.0 $\mathrm{m} / \mathrm{s}$ . The vertical component of Earth's magnetic field in this region is 40.0$\mu \mathrm{t}$ directed downward. Calculate the induced emf between the ends of the wire and determine which end is positive.

0.0012 \mathrm{V}

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Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

McMaster University

we're told that we have a wire with a length L of two meters held in east west direction and it moves horizontally at a velocity V of 15 meters per second. And the vertical component of the Earth's magnetic field in this region is 40. Might, uh, micro Tesla or 40 times 10 to the minus six Tesla. So this is the perpendicular magnetic field causes perpendicular to the motion or the perpendicular to the motion or the velocity of the wire. Okay. Were asked here to calculate the induced in at a M f between the end of the wire and determine which end of the wire is positive. Okay, so the earth's vertical component acting downward, and the velocity on the wire is northward direction. Therefore, the angle between the magnetic field and the velocity of the wire is 90 degrees. So the expression for the emotional IMF, when the magnetic field is perpendicular to the velocity of the wire, can be given as e M. F is equal to the perpendicular magnetic field times the length of the wire times the velocity. Okay, well, we know all of these values here, so therefore we can go ahead and just plug them in and it comes out to be 1.2 times 10 to the minus three. Oh, in the units here, our votes. Okay, so we can go ahead and box it in as the solution to the magnitude of the induced ium f, but were also asked to figure out which end is the positive end. So use the right hand rule to identify the direction of the magnetic force from the right hand rule. The fingers represent the direction of motion of the object or the velocity. Okay. And folding of the fingers represents the direction of the magnetic field, and the thumb represents the direction of the magnetic force. So assume the fingers air shown in the northward direction or in the direction of the velocity. So the fingers air curled downward direction or the direction, the magnetic field and the thumb that represents the direction of the magnetic force should be the direction in the west for direction. This magnetic force tends to move the positive charge in the western direction. So hence the positive charge must be present at the west end of the of the wire, so we can say, uh, that the magnetic force. So we'll say it like this. We'll say magnetic force and therefore positive charge. Let's say the magnetic force is in the westward direction. Therefore, the positive charge you started new line here. Positive charge is at the west end of the wire so we can go ahead and box it in is the second part of the solution to our question since we were asked to find the end at which the positive charge is accumulating.