Exam 3 Study Guide PDF

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Study guide for exam three in general physics 2. Includes homework and example problems....

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Exam 3 Study Guide Module 7a General Info Magnets and Magnetic Field Rules: 1. Each magnet is a dipole with an N and S pole - magnets with monopoles have not been observed. 2. Magnetic field lines help us visualize the magnetic field present in space. 3. Magnetic field lines emerge from the N poles and enter at the S pole, continuing through the magnetic. 4. The direction of a magnetic field at any point in space is obtained by drawing tangent to the field lines. 5. The strength of a magnetic field is given by the density/bunching of lines 6. Magnetic field lines do not cross. Earth’s Magnetic Field: - Since the north poles of compass magnets point north, the magnetic pole there is actually a south pole. - .5 x 10-4 tesla - Protects the atmosphere from solar wind, has reversed 183 times over the last 83 million years, moves 55 km per year (used to be 15), heading from canada into siberia. Magnetic Force on Moving Charges: - Magnets exert forces on moving particles and moving charges create magnetic fields. F = |q|vB sin 𝜃 F = magnetic force q = charge v = velocity B = magnetic field Use Gauss (G) as a unit to describe a magnetic field (1 T = 104 G) Right Hand Rule: (X - into the page) (• - out of the page) 1. Align thumb along V 2. Align fingers along B 3. The force of a positive charge comes out of the palm and the force of a negative charge comes out the back of your hand.

Module 7b General Info Motion of Charged Particles in a Magnetic Field: - In a magnetic field the force on a positive charge is perpendicular to the B field leading to very different circular motions. (Unlike the electric field, a magnetic field cannot do work on a particle and the particle’s speed remains constant) F = qvB sin 𝛳= mv2/r r = mv / qB - Larger velocity, bigger the radius In a mass spectrometer, ions of different mass and charge move in circles of different radii, allowing separation of different isotopes of the same element. - Heavier, larger radius Lighter, smaller radius Synchrotrons and Cyclotrons Both are charged particle accelerators. High speed particles contain high energy and can be used to create isotopes, treat tumors/cancer, determine material makeup. Cyclotron: accelerate protons up to 730 MeV. Synchrotron: accelerate protons up to 1 trillion eV, much bigger diameter Magnetic Force Exerted on a Current-Carrying Wire I = current l = length of wire B = magnetic field F = ILB sin 𝛳 = mg

𝛳 = angle bt B and I Parallel: sin 𝛳 = 0 Perpendicular: sin 𝛳 = 1

Right Hand Rule: (X - into the page) (• - out of the page) 1. Align fingers along magnetic field (B) 2. Align thumb along direction of current (I) 3. Direction of force comes out of the palm

Loops of Current and Magnetic Torque T = (IhB)(w/2) + (IhB)(w/2) = IB(hw) or IBA T = NBIA sin 𝜃 - 𝜃 is the angle between the magnetic field direction (B) and the normal to the plane of the loop. To increase torque, a long wire may be wrapped in aloop many times (turns N) Torque is independent of the shape of an area

Module 7c General Info Magnetic Fields Produced by Current Sources (Electromagnets) “Ampere’s Law” - Mo - permeability of free space = 4 x 10-7 . Right Hand Rule for magnetic fields (B): 1) Point thumb along the wire in the direction of current I 2) Fingers are now curing around the wire in the direction of the magnetic field. Force Between Two Long Straight Wires Parallel wires with current in the same direction attract each other Parallel wires with current in opposite directions repel each other Current Loops and Solenoids Solenoid: series of current loops formed into a cylinder. On the outside there are few field lines and the magnetic field is weak. In the inside there are many field lines and a stronger B field. - Will act as a magnet only when a current flows through the coil. An attractive force between parallel loops with currents in the same direction and a repulsive force between parallel loops with currents in opposite directions. B = (uo) (N/l) (I) B = uo I / 2 pi r

Module 7 HW 1. Answer the following questions about magnetic fields a) Choose the correct statement

b) What is an acceptable ending to the following sentence, “Magnetic field lines…”

c) Which of the following arrangements produce an attractive force?

2. Consider the figure.

a) What is the direction of magnetic force on the current in A?

b) What is the direction of magnetic force on the current in B?

c) What is the direction of magnetic force on the current in C?

d) What is the direction of magnetic force on the current in D?

e) What is the direction of magnetic force on the current in E?

f) What is the direction of magnetic force on the current in F?

3. A wire carrying a 42.5 A current passes between the poles of a strong magnet so

that it is perpendicular to the field and experiences a 2.16 N force on the 4.25 cm of wire in the field. What is the average field strength (T)? 4. Consider a loop with 50 square turns that is 18 cm on a side and is in a uniform 0.65 T magnetic field. Find the current through a loop needed to create a maximum torque of 9.00 N⋅m. 5. A negative charge of q = -3.7 × 10-17C and m = 3.4 × 10-26 kg enters a magnetic field B = 0.75 T with initial velocity v = 340 m/s, as shown in the figure. The magnetic field points into the screen. a) Which direction will the magnetic force be on the charge?

b) Calculate the magnitude of the force F, in newtons.

c) Calculate the magnitude of the centripetal acceleration, a, in meters per square second.

d) Calculate the numerical value of the radius R, in meters.

6. Consider the magnetic fields and velocities of charged particle shown in the figure a) What is the direction of the magnetic force on a negative charge that moves as shown in (a)?

b) What is the direction of the magnetic force on a negative charge that moves as shown in (b)?

c) What is the direction of the magnetic force on a negative charge that moves as shown in (c)?

d) What is the direction of the magnetic force on a negative charge that moves as shown in (d)?

e) What is the direction of the magnetic force on a negative charge that moves as shown in (e)?

f) What is the direction of the magnetic force on a negative charge that moves as shown in (f)? 7. Consider the magnetic fields and forces shown in the figure a) What is the direction of the velocity of a postive charge that experiences the magnetic force shown in (a), assuming it moves perpendicular to B?

b) What is the direction of the velocity of a positve charge that experiences the magnetic force shown in (b), assuming it moves perpendicular to B?

c) What is the direction of the velocity of a positive charge that experiences the magnetic force shown in (c), assuming it moves perpendicular to B?

8.

An alpha particle (consisting of two protons and two neutrons), traveling at a speed of v = 1.5 x 105 m/s, enters a region of constant magnetic field of strength B = 1.1 T as shown in the figure. The direction of B is out of the image. The alpha follows a path that is a circular arc of radius r. a) In atomic mass units, what is the mass m of an alpha particle?

b) In units of elementary charge e, what is the electric charge q of an alpha particle?

c) In meters, what is the radius of curvature r of the path taken by the alpha particle?

9. Four current carrying wires are arranged in the corners of a square as shown in the picture. (right two corners are into the page left two corners are out of the page) The magnetic field in the center of the square is directed ___. 10. You are looking at a current carrying loop of wire laying flat on the table. As viewed from above, the current is moving in the clockwise direction. Magnetic field in the center of this loop is directed _____. 11. The hot and neutral wires supplying DC power to a light rail commuter train carry 800 A and are separated by 75.0 cm. What is the magnitude of the force (in N) between 65 m of these wires? 12. An infinitely long wire carries a current of I = 180 A. a) Consider a circle with a radius r and centered on the wire. Determine the magnitude of the magnetic field B at points along the circle in terms of I and r. (B is counter clockwise)

b) If r = 0.23 m, calculate the numerical value of B in tesla.

13. Suppose the starter cable of a car is carrying 155 A of current. Assume this cable is long and straight. How many meters from the cable must you be to experience a field less than the Earth’s (5.00 × 10-5 T)?

14. Consider two long wires with currents I1 = 7.6 A and I2 = 2.2 A, as shown in the figure. Let d = 0.095 m, a = 1.55 m. In this problem, consider out of the page to be the positive direction. a) Calculate the value of the magnetic field at point A, in Tesla.

b) What is the direction of BA?

c) Calculate the value of the magnetic field at point B, in Tesla.

d) What is the direction of BB?

15. A solenoid is made of N = 7500 turns, has length L = 45 cm, and radius R = 1.7 cm. The magnetic field at the center of the solenoid is measured to be B = 3.3 x 10-1 T. Find the numerical value of the current in milliamps.

16. Consider a long, closely wound solenoid with 10,000 turns per meter.What current, in amperes, is needed in the solenoid to produce a magnetic field inside the solenoid, near its center, that is 104 times the Earth’s magnetic field of 5.2 × 10-5 T?

Module 8a General Info Faraday’s Law of Induction Experiment: closing a switch in the primary circuit induces a current in the secondary circuit, but only while the current in the primary is changing. - No current in secondary when primary switch is left on - Direction of current in secondary changes when closing/opening switch (look for word “immediately” in question) - Observations connected to change in flux through coil. A current is induced in a coil or wire loop in the magnetic and coil are in relative motion → change in flux produces induced emf.

Emf (induced voltage) = -N (ΔΦ / Δt) = -N (ΔBA / Δt) ΔV = Emf = IR Emf = d2 cos 𝜃 (Bf - Bi) N = number of loops ΔΦ = change in flux Δt = time during movement occurred (neg sign is a result of Lenz’s law) Magnetic Flux N pole moving toward the coil → increasing magnetic flux N pole moving away from the coil → decreasing magnetic flux Stationary = no change in flux Φ (flux) = BA cos 𝜃 =B cos 𝜃 (Af - Ai) -

𝜃 is the angle between normal to the loop/plane and the B-field direction - Perpendicular to B = cos 0= max - Parallel to B = cos 90 = min

Module 8b General Info Lenz’s Law: The Induced current tends to maintain the original flux through a circuit. Steps for determining the direction an induced current: 1) Use the right hand rule to find external B - Fingers along ring, thump points up or down - OR - Line with current up will have x on right and • on left. 2) Determine if flux (or I) is increasing or decreasing given the provided info - Flux increases with N moving closer - Flux decreases with N moving farther 3) Find the induced B - Increase flux = opposite direction to external B - Decrease flux = same direction as external B 4) Use the right hand rule to determine direction (thumb along induced and curl fingers) - fingers curl in direction of the current flow. Magnet with north pole facing down and circular circuit below. - Magnet not moving = no flux = no induced emf / current - Magnet moving down = changing flux = induced up = ccw induced current - Magnet moving up = changing flux = induced down = cw induced current Magnet with south pole facing down and circular circuit below. - Magnet not moving = no flux = no induced emf / current - Magnet moving down = changing flux = induced down = cw - Magnet moving up = changing flux = induced up = ccw

Module 8c General Info Motional EMF When a conducting rod moves through a uniform magnetic field downward, the free electrons inside of the conductor experience magnetic force to the right, leaving a net positive charge on the left. F = qvB

E = vb

This produces an electric field due to charge separation that balances the magnetic force

ΔV = El

ΔV = Bvl

ΔΦ = BA cos 90 = Bl Δx B into the screen, A decreasing.. flux decreasing… induced same as B - Clockwise B into the screen, A increasing… flux increased… induced opposite of B - Counter Clockwise B out of the screen, A decreasing… flux decreasing… included same as B - Counter Clockwise B out of the screen, A increasing… flux increased… - Clockwise

AC Generators Mechanical input on a rotating loop and magnet produces a mechanical output. - This mechanical input can be from steam/gas/water turbines, windmills, etc E = NBA w sin wt w = angular speed of rotation of the coil

A = area of the coil

I (max) = E (max) / R

Working Principle of Transformer Used to change voltage in an alternating current. Step Up: Increases output voltage because it has more number of loops in secondary/output circuit than primary/input circuit Step Down: Decreases output voltage because it has lesser number of loops in secondary output/circuit than primary/input circuit

The transformer equation is based on the direct proportionality between the number of turns/loops in a coil and voltage generated. - Stepping up voltage results in lower current and stepping down is opposite

Module 8 HW 1. Consider the coil and wire depicted in the figure. What is the value of the magnetic flux through the coil due to the wire with a current I passing through it? Perpendicular to each other = 0 2. Consider the coils depicted in the figure. What is the value of the magnetic flux at coil 2 due to coil 1, which has a current I passing through it? Perpendicular to each other = 0

3. A loop of wire with radius r = 0.055 m is in a magnetic field with magnitude B as shown in the figure. B changes from B1 = 0.15 T to B2 = 4.5 T in Δt = 2.5 s at a constant rate. The resistance of the wire is R = 4 Ω. a. Calculate the numerical value of the change in magnetic flux, ΔΦ, in T⋅m2. ΔΦ= A ΔB = pi(r2)ΔB pi(.0552)(4.5-.15) = .041 b. Calculate the numerical value of the average emf, ε, induced in the loop in volts. emf = ΔΦ / Δt .041 / 2.5 = 1.64x10-2 c. Calculate the numerical value of the current induced in the loop, I, in amperes. I = E/R I = 1.64x10-2 / 4 = .00413 4. Suppose a 50 turn coil lies in the plane of the page in a uniform magnetic field that is directed into the page. The coil originally has an area of 0.25 m2 . It is

squished to have no area in 0.275 s. What is the magnitude of the average induced emf in volts if the uniform magnetic field has a strength of 1.5 T? emf = N (AΔB / Δt) (50) (.25)(1.5) / (.275) = 68.18 5. An emf is induced by rotating a 1000 turn, 16 cm diameter coil in the Earth’s 5.00 × 10-5 T magnetic field. What average emf is induced, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in 14 ms? emf = ΔΦ / Δt emf = N (AΔB / Δt) → 1000 pi(.16/2)2(5.00 × 10-5) / 14x10-3 = .0718 6. A wire carrying 425 A to the motor of a commuter train feels an attractive force of 3.9 × 10-3 N/m due to a parallel wire carrying 4.8 A to a headlight. How far apart are the wires in meters? F/L = uoI1I2 / 2pi(d) d = uoI1I2 / 2pi(F/L) → (4pi x 10-7 x 425 x 4.8) / (2pi x 3.9 × 10-3) = .105 7. A jet airplane with a 75.0 m wingspan is flying at 265 m/s.What emf is induced between the wing tips in V if the vertical component of the Earth’s magnetic field is 3.00 × 10-5 T? emf induced = BvL → (3x10-5)(265)75.0 = .596 8. Consider a conducting rod of length 29 cm moving along a pair of rails, and a magnetic field pointing perpendicular to the plane of the rails. At what speed (in m/s) must the sliding rod move to produce an emf of 1.15 V in a 1.75 T field? e = Blv → v = e / Bl = 1.15 / (.29 x 1.75) = 2.27 9. Suppose a conducting rod is 69.5 cm long and slides on a pair of rails at 2.5 m/s. What is the strength of the magnetic field in T if a 2 V emf is induced? e = Blv → B = e / lv → (2) / (.695) (2.5) = 1.15 10. A loop is placed in a region where the magnetic field is changing. At t = 0 s the magnetic field is 1 T directed into the page. Over a period of 2 s the field changes uniformly to 1 T directed out of the page. Which of the following describes the

direction, clockwise (CW) or counterclockwise (CCW), of the induced EMF in the loop? The induced emf must be in the opposite direction to the external field (which is out of the page). Using the right hand rule again, we see that in order to produce an induced magnetic field into the page, the current must be clockwise again. 11. A loop is placed near a current carrying wire as shown in the figure. Which of the following two scenarios will induce a counterclockwise EMF as shown?

12. Suppose you rotate a 1000 turn, 18 cm diameter coil in the Earth’s 5.00 × 10-5 T magnetic field. What is the peak emf generated in V, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in 7.5 ms? emf = NBA / L = 1000 x 5x10-5 x .092 pi / 7.5x10-3 4...