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19 Overview

• magnetic force fields & sources

• forces on charges & currents

• Homework:

• 3, 7, 10, 33, 45, 55, 75.

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Magnetic Field, B• SI Unit: tesla, T = N/A·m

• Direction shown below

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Magnetic Poles

• Do ______ have _____ electric charge

• _______________ plates easily make uniform electric fields.

• Uniform B field difficult to achieve

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Magnetic Force on Charge

• F = qvB sin θ

• ___________ points in direction of force on a ________________ charge (Flat RHR)

• Negative charge feels ________________ directed force

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Properties of the Magnetic Force

• F = qvB sin θ• Proportional to: charge, speed, field, &

sine of angle between v and B.• perpendicular to both v and B.• /

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Ex. An object with a charge of 2.0 mC is moving Ex. An object with a charge of 2.0 mC is moving perpendicular to a magnetic field of strength 1.0 T at perpendicular to a magnetic field of strength 1.0 T at a speed of 1.0 x 10a speed of 1.0 x 1033 m/s. a) Sketch the situation. b) m/s. a) Sketch the situation. b) Find the magnetic force on the particle. Find the magnetic force on the particle. c) Indicate the direction of the force on your sketch.c) Indicate the direction of the force on your sketch.

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Applications of Magnetic Force

• electric motor

• Mass spectrometer

• magnetohydrodynamic propulsion

• colliders

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Cyclotron Motion

• Magnetic force is __________________ to velocity

• causes a free charge to move in a circle

• Does no ___________

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Cyclotron Motion

• qvB = _____________

• radius of motion r = mv/qB

• period of motion = T ( vT = 2r )

• frequency = 1/T

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Ex. A particle, m = 1gram, v = 10m/s, q = 1mC, Ex. A particle, m = 1gram, v = 10m/s, q = 1mC, moves perpendicular to a uniform field B = 1.0 T moves perpendicular to a uniform field B = 1.0 T directed into the screen. Sketch the motion and directed into the screen. Sketch the motion and calculate its radius.calculate its radius.

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Magnetic Force on a Current Carrying Wire

• net magnetic force = net magnetic force on all moving charges

• qv = IL

• (C)(m/s) = (C/s)(m)

• F = ILB sin θ

• //

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Force on a Current Carrying Wire

• F = ILB sin θ

• Direction is given by a right hand rule

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Ex. A wire of length 1m is perpendicular to a uniform Ex. A wire of length 1m is perpendicular to a uniform magnetic field of strength 0.50 T. a) Sketch the situation. b) magnetic field of strength 0.50 T. a) Sketch the situation. b) Choose a direction for the current and indicate the direction Choose a direction for the current and indicate the direction of the force on the wire for your choice. c) If the magnitude of the force on the wire for your choice. c) If the magnitude of the force is 10 N, find the current in the wire.of the force is 10 N, find the current in the wire.

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Electric MotorsThe ILB force causes a motor coil to turn. Current The ILB force causes a motor coil to turn. Current ____________________________________ is changed by a split ring. is changed by a split ring.

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Torque on Coil

• area, A number of turns, N

• current in wires, I

• in field, B

• angle between coil normal & B: .

• torque = NIABsin.

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torque example

• Tesla Motors Car produces __________________ = 271 m·N NIAB = 271 m·N.

• estimated reasonable? specs:

• with B = 0.3T: NIA = 904.

• with A = 0.05sq.m.: NI = 18,000.

• with I = 20A: N = 900turns

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Straight Wire & Loop

r

IB o

2

R

INB o

center 2

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Solenoid

IL

NB ocenter

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Ferromagnetism

• Unmagnetized

• Induced

• Permanent

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Summary

• F = qvB sin = ILB sin (Flat RHR)

• B fields around wires (Curled RHR)

• B field inside a solenoid is nearly uniform

• electric motors utilize B force

• charge motion (v, I) causes B fields

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