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Magnetic Fields

Electric fields are not enough to explain everything in electrodynamics. It turns out that we need to consider a second field as well, called the magnetic field. Both stationary and moving charges generate an electric field, but only moving charges generate a magnetic field.


Magnetic fields appear outside the wires in which there is current flowing. A current is a flow of charge, that is, the quantity of charge moving past a point per unit of time. The units of current are [C/s = amperes = amps = A]. For most problems it does not matter whether we think of (negative) electrons moving left or of some positive charge moving right. In physics we generally think in terms of a positive charge moving, even though we know that it is the electrons which are moving. For this reason, if electrons are moving to the left along a wire, then we say the current is toward the right, since electrons have negative charge.
If a current is flowing in a wire, this generates a magnetic field outside the wire. This magnetic field points not toward, not away from, not along the wire, but tends to point around the wire. It is strongest near the wire, of course. We can remember its direction by applying the first hand rule: Use your right hand and point the thumb in the direction of the (positive) current. Bend your fingers around so the tips are as close to your wrist as possible. The fingers tend to point in the direction of the magnetic field. Figure 14-27 shows a current flowing to the right. The small arrows show the direction of the magnetic field. Figure 14-28 shows a current coming out of the page. Again, the arrows show the magnetic field. A circle with a dot in it often denotes a vector coming out of the page, like an incoming arrow. A circle with a cross in it denotes a vector going into the page, like the feathers of a receding arrow.


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Figure 14-27

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Figure 14-28


Certain materials, such as iron, generate magnetic fields as well, and at first glance there do not seem to be any currents here. The reason for magnetic fields in these cases is subtle and involves the current of electrons about the nucleus. This is almost certainly beyond the scope of the MCAT.
A charge sitting still in a magnetic field experiences no force. Furthermore, a moving charge experiences a magnetic force only if its motion has a component perpendicular to the magnetic field. In that case the particle experiences a force which is perpendicular to the magnetic field and to the charge’s path. Figure 14-29 shows a situation in which the magnetic field is coming out of the page and a proton is moving to the right.

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Figure 14-29

The second hand rule helps you to recall the direction of the force: For a positive particle, use your right hand. Your fingers point in the direction of the magnetic field, which you can remember because the four fingers look like the field lines of a magnet. Your thumb points in the direction that the particle is going, like a hitchhiker. Your palm (which you use for pushing) points in the direction in which the particle experiences a force. For a negative particle, use your left hand.
In brief, every point in the universe has two vectors sitting on it, one being the electric field and the other being the magnetic field. Just to help you visualize it, imagine going to a field in the Northern Hemisphere on a clear day and picking a point in the air. To a close approximation, the electric field points down with a magnitude 100 N/C and the magnetic field points south (0.5 gauss, if you must know, but we have not discussed units for the magnetic field).


Now the force on a particle due to a magnetic field is always perpendicular to the displacement of the particle. For this reason magnetic forces do no work (always we have cosφ = 0). If you ever encounter a question such as “How much work does the magnetic force … ?” you need read no further. The answer is zero.

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