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You have two wires, lying close together, carrying equal currents (I 1 = I 2 )in opposite directions. What is the strength of the magnetic field a great distance, r, from these two wires according to Ampere’s Law? B = 0 B = m o I 1 I 2 /2 p r B = m o (I 1 + I 2 )/2 p r

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  1. You have two wires, lying close together, carrying equal currents (I1 = I2)in opposite directions. What is the strength of the magnetic field a great distance, r, from these two wires according to Ampere’s Law? • B = 0 • B = mo I1 I2/2 p r • B = mo (I1 + I2)/2 p r • B = mo I1/2 p r • B=mo I2/2 p r I1 I2 B

  2. Correct Answer – A Ampere’s law gives us the result that the magnetic field around a wire carrying current I, at a distance r from the wire, is B = mo I / 2 p r . The right hand rule tells us that the field from one wire will point in the opposite direction from the field from the other wire, so if the currents are equal and the distances from the wires are approximately equal then the field produced by each wire will cancel each other, so B = 0

  3. Take the same two wires and run the current in the same direction in each. Now what does Ampere’s Law tell us about the magnetic field strength far from the two wires? • B = 0 • B = mo I1 I2/2 p r • B = mo (I1 + I2)/2 p r • B = mo I1/2 p r • B=mo I2/2 p r I1 I2 B

  4. Correct Answer – C Ampere’s Law tells us that the field along a closed loop depends on the total current flowing through the interior of the loop. So if the currents are in the same direction we simply add them to get the total field producing current (if we use our usual formula we also have to be sure the distance from each wire is about the same). B = mo (I1 + I2)/2 p r Another way to get the right answer is to simply get the field from each wire and then add them together. All fields and potentials follow the rule that if there is more than one field at a given point, the total field strength at that point is simply the sum of the individual fields.

  5. What sort of magnetic field strengths do you expect to find in your home? There are a lot of wires there carrying significant currents. The amount of current used to light a light bulb, for instance, is on the order of 1 A. To begin estimating the magnetic field in your home, let’s calculate the magnetic field felt when you are standing r = 1m away from a wire carrying I = 1 A of current. Keep in mind that mo = 4 p x 10-7T m/A. • B = 0 • B = 2 p x 10-7 T • B = 2 x 10-7 T • B = 4 p x 10-7 T • B = 1 T

  6. Correct Answer – C Since mo = 4 p x 10-7T m/A we see that the formula for magnetic field around a wire becomes B = 2 x 10-7 I/r = 2 x 10-7 T If I = 1 A and r = 1 m.

  7. There are, of course, many wires running through your house. Do all these fields add up? If you had a thousand wires in your house, wired in usual way, what do you think the magnetic field strength would be, roughly? • 0 • 10-7 T • 10-4 T • 1 T

  8. Correct Answer – B (A is also very good) Studies show that .1 mT = 10-7 T is a typical exposure to magnetic fields in the house, so apparently it is no worse then one feels near just one wire. Why is this? When your house is wired two wires have to run to each lightbulb or socket. One to carry the current out, the other to carry it back. Wound around each other their magnetic fields cancel each other out. So the wiring in your house contributes very little to your local magnetic field. Your appliances can’t be wired so neatly, so they contribute most of the magnetic field you experience, which is still not very great. Keep in mind also that these fields are extremely low frequency. It is not at all clear that our body reacts to them at all. Indeed we seem to be definitely not react to low frequency electric fields.

  9. So it seems that our wiring protects us from the menace of magnetic fields. But putting two current carrying wires of length L a distance r apart, carrying equal currents in opposite directions, causes them to repel each other. What are the chances that the electric wiring is going to come bursting out of the walls of your home? In the situation at left, what is the repeling force the magnetic field of one wire exerts on the other? • F = 0 • F = mo I1 I2 L / 2 p r • F = mo (I1 + I2) L/ 2 p r • F = mo I1 L / 2 p r • F = mo I2 L / 2 p r r I I L B F

  10. Correct Answer – B In this case the magnetic field produced by one wire is B = mo I1/ 2 p r, at the other wire (they are r apart). Now a current carrying wire which is exposed to such a field at right angles to it feels a force which we calculated to be F = I2 L B, where I2 is the current in the wire feeling the force, L is the length of the that wire, and B is the field it experiences. Therefore F = mo I1 I2 L / 2 p r = 2 x 10–3 N = 2 mN For two 10 m long wires a millimeter apart.

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