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Magnetic Force

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Moving Charge A charge in an electric field is subject to a force. Charge at rest or in motion In the direction of field A charge in a magnetic field is also subject to a force. Only charges in motion Perpendicular to force and velocity E B v

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Direction of Force Magnetic force is another kind of vector multiplication. Vector cross product yields a vector The magnitude is qvB sin . The direction points according to the right-hand rule. force points into the page More force = increasing deflection

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Vector Cross Product The vector cross product applies to any two vectors. The cross product is perpendicular to the plane holding the two vectors. The cross product is not commutative. Reversing the order gives an anti-parallel resultReversing the order gives an anti-parallel result

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Uniform Field The magnitude is qvB sin . q = 1.6 x 10 -19 C v = 5.0 x 10 6 m/s B = 3.0 T Angle between v and B is 30° F = 1.2 x 10 -12 N The direction is based on a positive charge going down. Down cross north is east Force vector points east An electromagnet produces a 3.0 T uniform magnetic field pointing horizontally north in the gap between its poles. A proton enters the field heading north at a downward 30° angle with a speed of 5.0 x 10 6 m/s. Find the magnitude and direction of the force.

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Particle Tracks Particles like electrons and protons turn in a magnetic field. Tracks are captured on film. Curvature is related to the velocity. Fermilab photo from the 15’ bubble chamber

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Circular Path A charge that moves perpendicular to a uniform field stays perpendicular to the field. Uniform circular motion The magnetic force is a centripetal force. Field into page

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Cyclotron The size of the circle assumes uniform circular motion. r = mv/qB q = 1.6 x 10 -19 C v = 5.0 x 10 6 m/s B = 3.0 T m = 1.6 x 10 -27 kg r = 1.7 x 10 -2 m The proton in the earlier example moves in a circular path. Find the radius of the circle. next

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