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Introduction to SAT II Physics - FreeExamPapers

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The Earth itself acts like a huge bar magnet. The presence of a magnetic field about the<br />

Earth allows us <strong>to</strong> use compasses that point northward, and creates a spectacular aurora<br />

over the northern and southern skies. But the magnetism of the Earth is quite<br />

complicated, and is still an active subject of research for geologists, so let us turn <strong>to</strong> the<br />

simpler cases of idealized charges and constant magnetic fields.<br />

Magnetic Force on Charges<br />

The questions on magnetism that you’ll find on <strong>SAT</strong> <strong>II</strong> <strong>Physics</strong> will deal for the most part<br />

with the reciprocal relationship between magnetic fields and moving charges. Generally,<br />

these questions will expect you <strong>to</strong> predict the motion of a charge through a magnetic field,<br />

or <strong>to</strong> calculate the magnitude of the magnetic force or magnetic field strength necessary<br />

<strong>to</strong> move a charge in a certain manner.<br />

Calculating Magnetic Force<br />

A magnetic field exerts a force on a moving charge. Given a magnetic field, B, and a<br />

charge, q, moving with velocity, v, the force, F, on the charge is:<br />

Magnetic field strength is measured in teslas (T), where 1 T = 1 N/A · m.<br />

You’ll notice that the force on a moving particle is calculated as a cross product of the<br />

particle’s velocity and the magnetic field’s strength. You can determine the direction of<br />

the vec<strong>to</strong>r by using the right-hand rule as follows: point the fingers of your right<br />

hand in the direction of the velocity vec<strong>to</strong>r and then curl them around <strong>to</strong> point in the<br />

direction of the magnetic field vec<strong>to</strong>r. The direction in which your thumb points gives you<br />

the direction of the vec<strong>to</strong>r.<br />

However, though q is a scalar quantity, it can affect the direction of the force vec<strong>to</strong>r. If q<br />

has a negative value, then has a negative value, and so the force vec<strong>to</strong>r will point<br />

in a direction opposite from what the right-hand rule might tell you.<br />

You can calculate the magnitude of the magnetic force without using the right-hand rule,<br />

so long as you know the angle, , between the velocity vec<strong>to</strong>r and the magnetic field<br />

vec<strong>to</strong>r:<br />

The sin term is important, because it lets us see very quickly that there is no force if a<br />

charge moves parallel <strong>to</strong> a magnetic field, and that the greatest force occurs when a<br />

charge moves perpendicular <strong>to</strong> the magnetic field.<br />

EXAMPLE<br />

247

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