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Magnetic Force on Freely Moving Charges And Third Left Hand Rule POS Checklist explain, qualitatively and quantitatively, how a uniform magnetic field affects a moving electric charge, using the relationships among charge, motion, field direction and strength, when motion and field directions are mutually perpendicular. predict, using appropriate hand rules, the relative directions of motion, force and field in electromagnetic interactions Field Theory Any object with mass produces a gravitational field The force of gravity acts in the same direction as the G-field Any object with charge produces an electric field The force of electricity acts in the same direction as the E-field Any magnet/current carrying wire produces a magnetic field What direction does the magnetic force work in? The FB acts perpendicularly to the current and the B-field This direction can be found using the 3rd Left Hand Rule: rd 3 Left Hand Rule Important Facts about Fm Fm acts on the e¯ in wire, not on the wire itself ∴ the wire is not required for Fm to exist Fm acts on any moving charge. Fm can act on any moving charge, even if it is not in a wire Formula for Magnitude of Deflection: Fm qv B q = magnitude of charge (C) v⊥ = speed of the charge, ⊥ to B field (m/s) B = external magnetic field (T) C mT Note : N s Fm is perpendicular to both v and B If B v : then Fm is at a max Fm qv B perpendicular If B v : then Fm =0 Fm qv B parallel Solution: Solution: Solution: Solution: Ex. 2 A proton is moving 8.60 × 104 m/s North through a 1.20 T perpendicular magnetic field directed vertically upward. Find its acceleration (mag and dir). Direction of a: Magnitude of F: Fm qv B 19 Fm (1.60 10 C )(8.60 10 m / s)(1.20T ) Fm 1.6512 10 14 4 N Acceleration Fnet Fm 14 Fnet 1.6512 10 N a 27 m 1.67 10 kg a 9.88742.... 10 m / s 9.89 10 m / s 12 2 12 2 Diploma Diploma Uniform Circular Motion If Fm is the only force on the charge If Fm is the only force, then, Fm is Fnet What is the direction of the acceleration? How do you know? Newton's 2nd Law: a is in the same direction as Fnet Notice that a v This is called centripetal acceleration. Centripetal acceleration Change in direction, but no change in speed. Thus it is uniform circular motion. Fm is called the centripetal force since it is responsible for moving the charge in a circle Notice that both Fm and ac act toward the center of the circle Equation: mv Fc r Fm qv B Fm Fc mv qv B r mv qB r 2 2 Example: An electron traveling at 5.00 x 106 m/s enters a magnetic field of 2.00 x 10-4 T at 90. Determine the radius of the path followed by the electron within the magnetic field.