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1.Moving electric charges produce magnetic fields, B B measured in Tesla (1T = 10 4 Gauss) Earth’s B field ~ 0.5 Gauss Largest permanent magnet ~ few T Largest man-made magnet ~ 20 T 2.Magnetic fields exert forces on moving electric charges

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Magnetic Force F = qvBif v ┴ B F = 0if v ║ B F = qvB sin ,if v makes angle with B Right hand rule for direction In case where v ┴ B, the trajectory is a circle In general, the trajectory is a helix

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Group Problem Suppose a proton has a velocity v = 10 6 m/s to the right perpendicular to a uniform magnetic field B = 2 T (take B directed up out of the paper ). a)What is the force on the proton? (magnitude and direction ) b)What will be the path of the proton? c)Find the radius of the circular orbit of the proton

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Forces & Torques on a Current Loop In general, = B sin , where is the angle between (perpendicular to the area) and B

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Group Problem A long straight wire lies along the x-axis and has a constant current of 3A in the + direction. a)Find B at a point 2m from the wire b)Find B at a point 1.5 m from the wire in the opposite direction from (a) c)Find the force on an electron located at the point in (a) and moving with a velocity of 3 m/s perpendicularly away from the wire. d)Find the force/length on a second long straight wire lying parallel to the first 3 m away and having a current of 2A in the opposite (-) direction

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