Concept Questions with W11D2 Concept Questions Review W11D2 2 Concept Questions with W7D1 W07D1 Magnetic Dipoles, Force and Torque on a Dipole, Experiment 2 W07D1 Magnetic Dipoles, Torque and Force on a Dipole, Experiment 2: Magnetic Dipole in a Helmholtz Coil Reading Course Notes: Sections 8.4,8.11.6, 9.5 9.9 4 Concept Question: Magnetic Field Lines The picture shows the field lines outside a permanent magnet The field lines inside the magnet point: Concept Q. Answer: Magnetic Field Lines Answer: 1. They point up inside the magnet 1. Up 2. Down 3. Left to right 4. Right to left 5. The field inside is zero 6. I don t know 5 Magnetic field lines are continuous. E field lines begin and end on charges. There are no magnetic charges (monopoles) so B field lines never begin or end 6 1
Concept Question: Parallel Wires Concept Q. Answer: Parallel Wires Consider two parallel current carrying wires. With the currents running in the opposite direction, the wires are 1. 2. 3. 4. 5. Answer: 1. The wires are repelled I1 creates a magnetic field into the page at wire 2. That makes a force on wire 2 to the right. attracted (opposites attract?) repelled (opposites repel?) pushed another direction not pushed no net force I don t know I2 creates a magnetic field into the page at wire 1. That makes a force on wire 1 to the left. 7 Concept Question: Dipole in Uniform Magnetic Field 8 Concept Q. Answer: Dipole in Field From rest, the coil in a uniform magnetic field above will: 1. 2. 3. 4. 5. 6. 7. 8. rotate wise, not move rotate counterclockwise, not move move to the right, not rotate move to the left, not rotate move in another direction, without rotating both move and rotate neither rotate nor move I don t know 9 Concept Question: Dipole in Field Answer: 1. Coil will rotate clockwise (not move) No net force so no center of mass motion. BUT Magnetic dipoles rotate to align with external field (think compass) 10 Concept Q. Answer: Dipole in Field The current carrying coil above will feel a net force 1. 2. 3. 4. upwards downwards of zero I don t know Answer: 2. Feels downward force. The forces shown produce a net downward force 11 12 2
Concept Question: Dipole in Helmholtz Concept Q. Answer: Dipole in Helmholtz A dipole pointing along the positive x-direction and located at the center of a Helmholtz coil will feel: 1. a force but not a torque. 2. a torque but not a force. 3. both a torque and a force. 4. neither force nor torque. Answer: 2. a torque but not a force. The Helmholtz coil makes a UNIFORM FIELD. Dipole feels only torque (need gradient for force). Concept Question: Dipole in Anti- Helmholtz Coil A dipole pointing along the positive z-direction and located at the center of an anti- Helmholtz coil will feel: 1. a force but not a torque. 2. a torque but not a force. 3. both a torque and a force. 4. neither force nor torque. Concept Q. Answer: Dipole in Anti- Helmholtz Coil Answer: 1. A force because there is a nongradient of the magnetic field but no torque because the magnetic field at the center is zero. Concept Questions with W09D1: Sources of Magnetic Fields: Ampere s Law W9D1 Today s Reading Assignment Course Notes: Sections 10.1-10.6 18 3
Concept Question: Line Integral The integral expression C.Q. Answer: Line Integral 2. A line integral by definition is the sum 1. is equal to the magnetic work done around a closed path. 2. is an infinite sum of the product of the tangent component of the magnetic field along a small element of the closed path with a small element of the path up to a choice of plus or minus sign. 3. is always zero. 4. is equal to the magnetic potential energy between two points. We need to make a choice of integration direction (circulation) for the line integral. The small line element is tangent to the line and points in the direction of circulation. The dot product therefore is the product of the tangent component of the magnetic field in the direction of the line element. So the answer depends on which way we circulate around the path. 5. None of the above. 19 20 Concept Question: Ampere s Law C.Q. Answer: Ampere s Law Integrating B around the loop shown gives us: 1. a positive number 2. a negative number 3. zero 21 Answer: 3. Total enclosed current is zero, so 22 Concept Question: Ampere s Law C.Q. Answer: Ampere s Law Integrating B around the loop in the clockwise direction shown gives us: 1. a positive number 2. a negative number 3. zero Answer: 2. Net enclosed current is out of the page, so field is counter-clockwise (opposite to circulation direction) 23 24 4
Concept Questions with W09D2: Faraday s Law W9D2 Today s Reading Assignment Course Notes: Sections 9.3-9.4, 9.6 26 Concept Question: Loop in Uniform Field Concept Q. Ans.: Loop in Uniform Field While a rectangular wire loop is pulled upward though a uniform magnetic field B field penetrating its bottom half, as shown, there is Answer: 1. The motion changes the magnetic flux through the loop. The magnetic flux is decreasing in time as more of the loop enters a region of zero magnetic field. According to Faraday s Law there is an induced current through the loop. 1. a current in the loop. 2. no current in the loop. 3. I do not understand the concepts of current and magnetic field. 4. I understand the concepts of current and magnetic field but am not sure of the answer. 27 28 Concept Q.: Loop in Uniform Field Concept Q. Ans.: Loop in Uniform Field While a rectangular wire loop is pulled sideways though a uniform magnetic field B field penetrating its bottom half, as shown, there is Answer: 2. The motion does not change the magnetic flux through the loop. The magnetic flux is constant in time. According to Faraday s Law there is no induced current through the loop. 1. a current in the loop. 2. no current in the loop. 3. I do not understand the concepts of current and magnetic field. 4. I understand the concepts of current and magnetic field but am not sure of the answer. 29 30 5
Concept Question: Loop Concept Question Answer: Loop The magnetic field through a wire loop is pointed upwards and increasing with time. The induced current in the coil is Answer: 1. Induced current is clockwise This produces an induced B field pointing down over the area of the loop. 1. Clockwise as seen from the top 2. Counterclockwise 31 The induced B field opposes the increasing flux through the loop Lenz s Law 32 Concept Question: Moving Loop Concept Q. Answer: Moving Loop A circuit in the form of a rectangular piece of wire is pulled away from a long wire carrying current I in the direction shown in the sketch. The induced current in the rectangular circuit is 1. Clockwise 2. Counterclockwise 3. Neither, the current is zero 33 Answer: 1. Induced current is clockwise B due to I is into page; the flux through the circuit due to that field decreases as the circuit moves away. So the induced current is clockwise (to make a B into the page) Note: I ind dl x B force is left on the left segment and right on the right, but the force on the left is bigger. So the net force on the rectangular circuit is to the left, again trying to keep the flux from decreasing by slowing the circuit s motion 34 Concept Question: Faraday s Law: Loop A coil moves up from underneath a magnet with its north pole pointing upward. The current in the coil and the force on the coil: Concept Question Answer: Faraday s Law: Loop Answer: 3. Current is clockwise; force is down The clockwise current creates a self-field downward, trying to offset the increase of magnetic flux through the coil as it moves upward into stronger fields (Lenz s Law). 1. Current clockwise; force up 2. Current counterclockwise; force up 3. Current clockwise; force down The I dl x B force on the coil is a force which is trying to keep the flux through the coil from increasing by slowing it down (Lenz s Law again). 4. Current counterclockwise; force down 35 36 6
Concept Questions with W10D1: Inductance and Magnetic Field Energy W10D1 Today s Reading Assignment W10D1 Inductance & Magnetic Energy 38 Concept Question: Solenoid Concept Q. Ans.: Solenoid A very long solenoid consisting of N turns has radius R and length d, (d>>r). Suppose the number of turns is halved keeping all the other parameters fixed. The self inductance 1. remains the same. 2. doubles. 3. is halved. 4. is four times as large. 5. is four times as small. 6. None of the above. 39 Solution 5. The self-induction of the solenoid is equal to the total flux through the object which is the product of the number of turns time the flux through each turn. The flux through each turn is proportional to the magnitude of magnetic field which is proportional to the number of turns per unit length or hence proportional to the number of turns. Hence the selfinduction of the solenoid is proportional to the square of the number of turns. If the number of turns is halved keeping all the other parameters fixed then he self inductance is four times as small. 40 7