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Physics 212 Lecture 12 Today's Concept: Magnetic Force on moving charges.

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1 Physics 212 Lecture 12 Today's Concept: Magnetic Force on moving charges

2 How about the fact that soon our planet's magnetic field will turn on it's end and switch polarity, if it doesn't disappear in the process that is, like it did for Mars. This flip will confuse animals that rely on internal compasses for migration. Also, due to the standard anomalies in polarity prior to the flip (see graphic at etic/reversals.html) our field will weaken enough to make cancer even more prevalent that it is currently from increased exposure to radiation. Also these anomalies will create multiple north and south poles covering much of the upper northernand lower southern hemisperes in auroras at night. Also, the weakening of the magnetic field may allow radiation to interfere with satellite transmissions. Hello cable TV! And most importantly, after the flip our compasses will point south.

3 Today’s Plan: 1)Review of magnetism 2)Review of cross product 3)Example problem Key Concepts: 1)The force on moving charges due to a magnetic field. 2)The cross product.

4 Magnetism I

5 Magnetic Observations N S Bar Magnets Compass Needles Magnetic Charge? S N N S cut in half

6 The earth is a big (weak) magnet

7 Compass needle deflected by electric current I Magnetic fields created by electric currents Magnetic fields exert forces on electric currents (charges in motion) VV I I F F V V I I F F Magnetic Observations

8 Magnetism & Moving Charges All observations are explained by two simple equations: Today Next Week

9 Cross Product Review Cross Product different from Dot Product –A ● B is a scalar; A x B is a vector –A ● B proportional to the component of B parallel to A –A x B proportional to the component of B perpendicular to A Definition of A x B –Magnitude: ABsin  –Direction: perpendicular to plane defined by A and B with sense given by right-hand-rule

10 Remembering Directions: The Right Hand Rule x y z B F v

11 Magnetic Force x y z B F screen x y z B v +q

12 VV I I F F Magnetic Force

13 Three points are arranged in a uniform magnetic field. The B field points into the screen. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: Since it has no velocity, there is no magnetic force.

14 Three points are arranged in a uniform magnetic field. The B field points into the screen. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: If my finger point in the direction of velocity, and I curl my fingers toward the electric field, my thumb points left.

15 Motion of Charge q in Uniform B Field x x x x x x x Uniform B into page Force is perpendicular to v –Speed does not change –Uniform Circular Motion Solve for R: q v F q v F q v F q v F R

16

17 The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure. Right hand rule. Put thumb in same direction of v and palm in direction of force (right). This shows the magnetic field points out of the page.

18 The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure. It turns sharper...the stronger the field the sharper the turns

19 Calculation A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? Conceptual Analysis –What do we need to know to solve this problem? (A) Lorentz Force Law (B) E field definition (C) V definition (D) Conservation of Energy/Newton’s Laws (E) All of the above X X X X X X X X X B B x0x0 x0x0 exits here enters here d q, m –Absolutely ! We need to use the definitions of V and E and either conservation of energy or Newton’s Laws to understand the motion of the particle before it enters the B field. –We need to use the Lorentz Force Law (and Newton’s Laws) to determine what happens in the magnetic field. E

20 Calculation Strategic Analysis –Calculate v, the velocity of the particle as it enters the magnetic field –Use Lorentz Force equation to determine the path in the field as a function of B –Apply the entrance-exit information to determine B A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? X X X X X X X X X B B x0x0 x0x0 exits here enters here d q, m E

21 What is v 0, the speed of the particle as it enters the magnetic field ? (A) (B) (C) (D) Why?? –Conservation of Energy Initial: Energy = U = qV = qEdInitial: Energy = U = qV = qEd Final: Energy = KE = ½ mv 0 2Final: Energy = KE = ½ mv 0 2 –Newton’s Laws a = F/m = qE/ma = F/m = qE/m v 0 2 = 2adv 0 2 = 2ad X X X X X X X X X B B x0x0 x0x0 exits here enters here d q, m E

22 Why?? –Path is circle ! Force is perpendicular to the velocityForce is perpendicular to the velocity Force produces centripetal accelerationForce produces centripetal acceleration Particle moves with uniform circular motionParticle moves with uniform circular motion X X X X X X X X X What is the path of the particle as it moves through the magnetic field? (A) (B) (C) X X X X X X X X X B B x0x0 x0x0 exits here enters here d q, m E

23 What is the radius of path of particle? (A) (B) (C) Why?? X X X X X X X X X R xoxo B B x0x0 x0x0 exits here enters here d q, m E

24 Why?? (A) (B) (C) (D) What is B in terms of v, x 0, q and m? X X X X X X X X X B B x0x0 exits here enters here d q, m E We already found that

25 Some not-so-good pictures claiming to illustrate the RHR…


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