1. Magnetic Field PH 203 Professor Lee Carkner Lecture 15

2. 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 

3. 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 

4. 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

5. 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

6. 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

7. 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?

8. 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

9. 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 (  )

10. 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 

11. Charged Particle in Field q v B 

12. 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 ~

13. 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

14. 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

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

16. 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

17. 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 

18. 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