Chapter 10 Electricity and Magnetism Part II
How does the right hand rule for magnets work?
Thumb: points in direction of velocity Fingers: Point your fingers in the direction of B Palm: for positive charges, it points the direction. For negative charges, points in the opposite direction
RMS voltage equation
V(rms) = v(max) / sqrt 2 = V/sqrt 2
All magnetic forces can do is make the charged particle _________ their direction
change
What causes a magnetic field?
flow of charged particles
Clockwise current produces a magnetic filed that points _______ the page
into
When current goes to the left, the magnetic field lines go _______ the page
into
Magnetic field is ________ proportional to radius
inversely
What are examples of ferromagnetic materials?
iron, cobalt, nickel
Since no work is being done, the _______ energy is constant
kinetic
Are there such things as magnetic monopoles?
no
When voltage is positive, the current flows in ______ direction. When the volt hare is negative, the current flows in the ________ direction
one opposite
Counterclockwise current produces a magnetic field that points ________ of the page
out
With current pointing to the right, the magnetic field lines go ________ the page
out (LIRO) (left into, right out)
The magnetic field inside a solenoid is _______ to the central axis
parallel
What are diamagnetic materials?
possess no unpaired electrons and are slightly repelled by a magnet
What are paramagnetic materials?
possess some unpaired electrons and become weakly magnetic in an external magnetic field
Magnetic field is ________ to current
proportional
What is RMS current?
room mean square current
A proton is injected with velocity v into a region of constant magnetic field B that points out of the plane of the page. The direction of v is to the right, in the plane of the page, as shown in the diagram below. A. Find the subsequent motion of the proton
thumb: right fingers: out of the page palm: down the page
Homes are typically supplied with 110 V rms. What is the maximum voltage?
v rms = vmax / sqrt 2 v max = v rms x sqrt 2 v max = 110 x sqrt 2 v max = 110 x 1.4 v max = 154 V
What are examples of diamagnetic materials?
water, plastic
The North Pole of a magnet wants to line up _______ the direction of an external magnetic field
with
What is alternating current?
A flow of electric charge that regularly reverses its direction.
A particle with negative charge -q moving with a speed v0 enters a region containing a uniform magnetic field B. If the vector v0 makes an angle 30 degrees with B, what is the particle's speed 8 seconds after entering the field? A. V0/4 B. V0 C. 2v0 D. 4v0
B; Magnetic forces do no work and therefore do not alter the speed
A particle with a positive charge q and mass m moving with speed v undergoes uniform circular motion in a constant magnetic field B. If the radius of the particle's path is r, which of the following expressions gives the particle's orbit period (in other words, the time required for the particle to complete on revolution? A. 2(pi)/qvB B. 2(pi)m/qB C. qvB/2(pi)m D. qB/2(pi)m
B; qvB = mv^2/r r = mv/qB T = 2pir/v T = 2(pi)(mv/qb) / v v cancels out T = 2(pi)(m) / qB
What does an x or an x with a circle around it signify?
Into the page
Magnetic force equation
F(B) = qvB F(B) = magnetic force (N) q = charge (C) v = speed (m/s) B = magnetic field (T, or N/Am)
The magnitude of the Earth's magnetic field is roughly 1 gauss at the surface (1 G = 10^-4 T). If a proton moving with a speed of v = 5 x 10^6 m/s in the atmosphere experiences a magnetic field strength of .5G, what force (magnetic or gravitational) has the greater effect? (Mass of proton 1.7 x 10^-27 N)
F(grav) = mg F(grav) = (1.7 x 10^-27)(10) F(grav) = 1.7 x 10^-26 N FB = qvB FB = (1.6 x 10^-19)(5 x 10^6)(.5 x 10^-4 T) FB = 4 x 10^-17 N FB >> Fg
How do you find the radius in a magnetic field?
FB = FC qvB = mv^2/r qB = mv/r r = mv/qB
Force equation on a current carrying wire
FB = ILB sin theta I = current L = length B = magnetic field Theta = angle between L and B
Magnitude of magnetic force equation
FB = |q|vB sin theta
What are ferromagnetic materials?
Ferromagnetic describes materials in which the magnetic spins of nearby atoms tend to align with one another, resulting in a permanent magnet.
RMS current equation
I(rms) = I(max)/sqrt2 = I /sqrt 2
Magnetic field lines curl around and re enter the magnet at the end designated the ________ pole
South
What is the unit of magnetism?
Tesla, or N/Am
The figure below shows a charged parallel plate capacitor with a uniform electric field, E, in the space between its plates. A uniform magnetic field, B, is also produced in the space between the capacitor plates by another device. At what speed would an electron need to travel between the plates in order to pass through undeflected? Electron is moving to the left Magnetic field is going into the page A. E/B B. B/E C. EB D. EB^2
A; E points toward the (-) end B is into the page electron is moving to the right FB = directed DOWN the page FE = directed UP the page FB = FE qvB = qE vB = E v = E/B, choice A
A wire loop lying on a table carries a counterclockwise current. A bubble machine is poised over the edge of the loop and fires a stream of tiny negatively charged bubbles horizontally across the center of the loop, travelling along a diameter from south to north. What is the direction of the magnetic force from the loop on the bubbles? A. The magnetic force is to the west. B. The magnetic force is to the east. C. The magnetic force is vertically up away from the table. D. The magnetic force is vertically down toward the table.
A; Find the direction of the magnetic field from the wire loop using the right hand rule. The field points up out of the table in the middle of the loop. Once the magnetic field is found, find the direction of the magnetic force on the bubbles using the left hand rule (since the bubbles are negatively charged) to determine the direction of the force is to the west (to the left if north faces away from the body). Counter clockwise current B = out of the page (imagine wrapping your fingers around a wire) Palm: west
An alternating current (AC) circuit consists of an alternating voltage source with a maximum voltage of 28 V and a maximum current of 7 A. What is the average power provided by the voltage source? A. 98 W B. 139 W C. 196 W D. 400 W
A; Average power for an AC circuit is I rmsV rms where I rms = I max / √2 and V rms= Vmax / √2. In this case, power = (7 / √2)(28 / √2) = 196 / 2 = 98 W. P = IV P = 7/sqrt 2 x 28/sqrt 2 P = (7/1.4) (28/1.4) P = (5)(20) P = 100 W
What are examples of paramagnetic materials?
Aluminum, platinum, gadolinium (MRI contrast)
An alternating current (AC) circuit contains a 6 ohm resistor with a maximum current of 4 A. What is the average power consumed by the resistor? A. 17 W B. 24 W C. 48 W D. 96 W
Average power for a resistor in an AC circuit is Irms2R where Irms = Imax / √2. In this case, power = (4 / √2)2(6) = 48 W. P = I^2R P = 4A / (sqrt 2) x 6 P = (4/1.4)^2 x 6 P = (3^2)(6) P = about 54 W, closest to choice C
A uniform magnetic field B exerts a force FB on a particle with charge q moving with velocity v through the field. Which of the following gives the magnetic force that the same field would exert on a particle of charge 2q moving with velocity -2v? A. -8FB B. -4FB C. 4FB D. 8FB
B FB = qvB FB = (2)(-2v)(B) FB = -4 FB
Two bar magnets are fixed in position, and a proton is projected with velocity v into the region between adjacent opposite poles, as shown below. Which of the following best illustrates the direction of the magnetic force on the proton at the position shown? First magnet is south on left and north on right proton is in-between the two magnets with v pointed down Second magnet has south on the left and north on the right A. Left B. Out of the page C. Into the page D. Right
B Thumb: down Fingers: right (because field lines point to the south) Palm: out of the page
Equation for a straight current carrying wire
B = u0I/2(pi)r B = magnetic field (T) u0 = permeability of free space (4pi x 10^-7 Tm/A) I = current (A) r = radius (m)
Equation for a current carrying wire for a circular loop
B = u0I/2r B = magnetic field (T) u0 = permeability of free space (4pi x 10^-7 Tm/A) I = current (A) r = radius (m) This equation only gives the magnetic field at the center of the loop
Particles with charge q and mass m are moved with velocity v in the negative zdirection through a magnetic field B pointing in the positive x direction. What is the magnitude of the acceleration on the particles due to the magnetic field? A. 0 B. qvB / m C. qv / Bm D. m / qvB
B; FB = ma qvB = ma a = qvB/m
An electron with charge -e and mass m moves with velocity v in the positive xdirection through an external magnetic field B that points in the negative zdirection. Assuming the effects of gravity are negligible, which of the following best describe the the electron's circular path as viewed from the positive z perspective (looking in the negative z direction)? A. Counterclockwise circle with radius mv / eB B. Clockwise circle with radius mv / eB C. Counterclockwise circle with radius eB / mv D. Clockwise circle with radius eB / mv
B; Since the charge is negative, the left hand rule is used to determine the direction of the magnetic force. The velocity is in the positive x direction and the magnetic field is in the negative z direction, so the initial magnetic force is in the negative y direction. Thus the acceleration on the electron results in the electron moving in a clockwise circle, eliminating choices A and C. Since the magnetic force is providing the centripetal force, the two forces can be set equal to each other, yielding mv2 / r = evB. Solving for r gives mv / eB. Clockwise because current is moving to the right
A sulfide ion, S2-, moving with a speed of v0 enters a region containing a uniform magnetic field B. If the vector v0 makes an angle of 30 degrees with B, what is the magnitude of the initial magnetic force on this ion? A. ev0B/4 B. ev0/2 C. ev0B D. 2ev0B
C; FB = qvB sin 30 FB = (2e)(v)(B)(.5) FB = ev0B
A high current power line is supported 10 m above ground and carries a current from West to East. A negatively charged balloon is released directly below the power line and begins to float straight up toward it. What is the direction of the magnetic force on the balloon due to the magnetic field surrounding the power line? A. North B. South C. East D. West
C; Find the direction of the magnetic field created by the wire using the right hand rule. The magnetic field under the wire points North. Once the magnetic field direction is found, find the direction of the magnetic force on the balloon using the left hand rule (since the balloon is negatively charged). The direction of the force on the balloon is to the East. Current: right Magnetic field: north (up the page) Palm: east
What is direct current?
Current that flows in only one direction
The figure below shows a long straight wire carrying a current, I. An electron from above the wire is initially parallel to it. Which of the following best illustrates the direction of the magnetic force on the electron at the position shown? Figure shows an electron moving the the left Current also points to the left A. Down the page B. Out of the page C. Into the page D. Up the page
D Thumb: left Fingers: out of the page for B (LIRO) Palm: up the page
The figure on the following page shows a circular loop of wire in the plane of the page, carrying a current I. A proton is projected with velocity v, such that v lies in a plane slightly above and parallel to the plane of the loop, as shown. Which of the following best illustrates the direction of the magnetic force on the proton at the position shown? Figure shows a clockwise current, proton moving to the left A. Up the page B. Out of the page C. Into the page D. Down the page
D thumb: left fingers: into the page palm: down
A particle with a positive charge q and mass m moving with a speed v undergoes uniform circular motion in a constant magnetic field B. If the radius of the particle's path is r, which one of the following expressions gives the magnitude of the momentum of the particle A. qB/r B. r/qB C. rB/q D. qBr
D; FB = FC qvB = mv^2/r qB = mv/r vm = qbR
A particle with charge q moves with velocity v through a region of space containing a uniform electric field E, and a uniform magnetic field, B. Which of the following expressions gives the total magnetic force on the particle? A. q(E + B) B. q(v x E + B) C. qv x (E + B) D. q(E + v x B)
D; FE = FB = 0 F total = qE + qVB F total = q (E + v * B)
The figure shown below shows a portion of long narrow solenoid carrying a current, I. An alpha particle (a) is projected with velocity down the central axis of the solenoid, as shown. Which of the following best illustrates the direction of the magnetic force on the alpha particle? Figure shows an alpha particle moving to the right in a solenoid A. Down the page B. Into the page C. Up the page D. None of the above
D; V is parallel to the magnetic field, so the magnetic force is 0
What kind of materials only have paired electrons
Diamagnetic
When is the magnetic force 0?
No charge or no speed
What work do magnetic forces do?
None! W = 0
By convention, the magnetic field lines emanate from the end of the magnet designated the _______ pole.
North
What does a dot or a circle with a dot represent when dealing with magnetism?
Out of the page
What is RMS voltage?
The value of direct voltage that produces the same power as the alternating voltage.
What happens if you split a magnet in half?
You get two separate and complete magnets each with a N-S pair.
What is a solenoid?
a coil of wire
What are magnetic fields?
a region around a magnetic material or a moving electric charge within which the force of magnetism acts.
What is a magnet?
any material that attracts iron or materials containing iron
