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Magnetic Field PH 203 Professor Lee Carkner Lecture 15

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HRW 7 Ed., P 27.20 Junction rule (at point d) i 1 +i 3 =i 2 Left loop: Right loop: Solve loop rule in terms of common variable, i 3 i 1 = ( 1 +i 3 R 3 ) / R 1 i 2 = (- 2 -i 3 R 3 ) / R 2 Put in numbers i 2 = -0.1 – 0.5i 3 1 = 4 V 2 = 1 V R 1 = 10 R 2 = 10 R 3 = 5

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HRW 7 Ed., P 27.20 Put in loop rule i 1 +i 3 =i 2 0.4 + 0.5i 3 + i 3 = -0.1 – 0.5i 3 2i 3 = -0.5 A i 3 is drawn backwards i 1 = 0.275 A These are drawn right V d –V c = i 2 R 2 = (0.025)(10) = +0.25 V 1 = 4 V 2 = 1 V R 1 = 10 R 2 = 10 R 3 = 5

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HRW 7 Ed., P 27.26 Power input to circuit is i V = Power dissipated by each resistor is i 2 R Voltage across A and B must equal voltage of 2 and 6 resistors i 1 = [78 – (6)(6)]/2= 21 A Junction rule i 1 = i 2 + i i 2 = 21 – 6 = 15 A i = 6 A V A -V B =78 V i1i1 i2i2

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HRW 7 Ed., P 27.26 Power input to circuit: Power dissipated by all resistors (i 2 R each): Since the resistors are using 1998 W and the applied voltage only supplies 1638 W, the box must be providing: 1998 – 1638 = 360 W i = 6 A V A -V B =78 V i1i1 i2i2

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Electricity and Magnetism Magnets exert a force on two types of objects: Both of these forces are due to the same fact: Magnetic fields produce a force on moving charges Moving charges produce a magnetic field Both electricity and magnetism are related to charge

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Vectors A magnet produces a magnetic field (B) The moving particle has a velocity (v) All three quantities are vectors What is the relationship between them? i.e., if the B field points one way and the charge is moving another way, what is the direction of the force?

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Right Hand Rule If v is your straight fingers, and you curl your fingers in the direction of B, F is your thumb F v B

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Vector Conventions The force on a negative particle is opposite that of a positive one Vectors going into the page are represented with a cross (X), vectors going out of a page are represented with a dot ( )

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Magnetic Force Magnitude The magnitude of the magnetic force depends on 4 things: The magnitude of the charge (q) The angle between the v and B vectors ( ) The force can be written as: F = qvB sin

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Charged Particle in Field q v B

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Magnetic Field We can use the expression for the force to write an expression for the magnetic field: B = F/qv sin We will often use a smaller unit, the gauss (G) Typical bar magnet ~ Earth’s magnetic field ~

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Crossed Fields Electric force: in direction of field If the E and B field are at right angles to each other, the forces will be in opposite directions

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Velocity Selector How could we get the forces to cancel out? If we “tune” B until the particle is not deflected, we can find the velocity

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Next Time Read 28.6-28-10 Problems: Ch 28, P: 9, 15, 16, 32, 46

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A resistor R and capacitor C are connected to a battery. If the resistor is replaced with a resistor of 2R, what happens to the time needed to charge the capacitor? A)It increases B)It decreases C)It depends on C D)It stays the same E)None of the above

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Over which time range does the charge on a capacitor increase the least (t=0 is uncharged) A)0 to 1 B)1 to 2 C)2 to 3 D)3 to 4 E)4 to 5

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Consider a simple circuit consisting of a battery and resistor. What will happen to the current if a voltmeter is used to measure the voltage through the resistor? What will happen to the current if a ammeter is used to measure the current through the resistor? A)increase, increase B)increase, decrease C)decrease, decrease D)decrease, increase E)You can’t tell without knowing the voltage of the battery

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