# Physics 212 Question Bank III 2010

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1 A negative charge moves south through a magnetic field directed north. The particle will be deflected (A) North. () Up. (C) Down. (D) East. (E) not at all.. A positive charge moves West through a magnetic field directed North. The particle will be deflected (A) North. () Up. (C) Down. (D) East. (E) not at all. The magnetic force on a moving charge is (A) proportional to electric charge. () perpendicular to velocity v. (C) proportional to speed v. (D) perpendicular to Magnetic Field. (E) all of the above.. The magnetic force on a moving charge is (A) proportional to magnetic charge. () perpendicular to velocity v. (C) inversely proportional to speed v. (D) parallel to Magnetic Field. (E) all of the above. A particle with a net electrical charge moving through a magnetic field will experience no force if (A) there is an electric field parallel to the magnetic field. () there is an electric field anti-parallel to the magnetic field. (C) the particle s velocity is parallel to the magnetic field. (D) the particle s velocity is perpendicular to the magnetic field. (E) the particle moves in a circle.. A current carrying wire in a magnetic field will experience no force if (A) the current is parallel to the magnetic field. () the current is perpendicular to the magnetic field. (C) there is an electric field parallel to the magnetic field. (D) there is an electric field anti-parallel to the magnetic field. (E) the magnetic field is not uniform. The motion of a charged particle in the presence of a (nearly uniform) magnetic field tends to be (A) helical (i.e. spiral), circulating about the magnetic field lines. () straight line, except when the charges bounce off of a magnetic field line as in magnetic mirrors. (C) rapidly slowing as the frictional effect of the magnetic force quickly uses up the particles kinetic energy. (D) rapidly increasing in speed as the particle is accelerated by the magnetic force. (E) completely unaffected by the magnetic field. 1

2 n order to use magnetic forces to levitate (i.e. magnetic force is upward against the force of gravity) a horizontal wire carrying a current towards the east, the magnetic field must be directed (A) Up. () Down. (C) North. (D) East. (E) South. The force on an electron traveling eastward through a northward directed magnetic field is (A) south. () north. (C) west. (D) down. (E) up. A velocity selector operates with charged particles moving from left to right, and a magnetic field directed upward. The electric field needed to balance the magnetic force (producing zero net force for charges moving at the correct velocity) should be (A) directed upwards. () directed downwards (C) directed into the page. (D) directed out of the page. (E) the answer will depend upon the mass and sign of the charge of the particles. Magnetic fields do not interact with (A) stationary electric charges. () moving electric charges. (C) stationary permanent magnets. (D) moving permanent magnets. (E) none of the above. The work done on a free electric charge by the magnetic force as the charge moves through the magnetic field will (A) depend upon the direction of the velocity of the charge. () depend upon the direction of the magnetic field. (C) depend upon the speed of the charge. (D) all of the above. (E) always be zero. The features (a) and (b) of the magnetization versus applied magnetic field plot at right are (A) hysteresis and permanent magnetization, respectively. () saturation and permanent magnetization, respectively. (C) hysteresis and saturation, respectively. (D) permanent magnetization and hysteresis, respectively. (E) none of the above. ( a ) M ( a ) 0 ( b )

3 . The magnetic field lines due to a straight wire carrying a current are (A) elliptical. () straight. (C) circular. (D) parabolic. (E) zero. The magnetic field of a long straight wire carrying a current into the page has field lines given by (A) () (D) (C) (E) There is no magnetic field unless the current is changing. The magnetic field at the center of a loop of wire carrying a current clockwise will be (A) clockwise. () counterclockwise. (C) into the page. (D) out of the page. (E) zero. A material which will weaken the net magnetic field (as compared to the same situation without the material) when an external field is applied is (A) paramagnetic. () ferromagnetic. (C) diamagnetic. (D) quasimagnetic. (E) paranormal. A material which will somewhat strengthen the net magnetic field (as compared to the same situation without the material) when an external field is applied is (A) paramagnetic. () pourrosmagnetic. (C) diamagnetic. (D) quasimagnetic. (E) paranormal.

4 Which property is associated with ferromagnetic materials? (A) Strong increase of magnetic field within the material. () Hysteresis. (C) Saturation. (D) Permanent magnetization. (E) all of the above. f a small permanent bar magnet is cut in half, the result is (A) one piece is a north magnetic pole and the other is a south magnetic pole. () neither piece retains any magnetic properties. (C) each piece would be a smaller bar magent, with both north and south poles. (D) trick question, since it is impossible to cut permanent magnets in half. (E) none of the above. A jet with a wingspan of 20m travels west at 1000 m/s through a region near the north magnetic pole where the magnetic field is 40x10-6 T downward. The magnitude of the motional emf induced across the wingspan is (A) 0 V. () 2x10-9 V. (C) 2x10-3 V (D).8 V. (E) none of the above. Two long parallel wires are separated by.05 m and both carry a current of 10 A in the opposite directions. The force exerted on a 1m section of one wire is (A) 4x10-3 N, towards the other wire. () 4x10-3 N, away from the other wire. (C) 4x10-4 N, along the wire, in the direction of the current. (D) 4x10-4 N, along the wire, in the opposite direction of the current. (E) none of the above. A pair of current carrying wires may be twisted around each other so that (A) the magnetic fields created by each wire will more effectively cancel. () the magnetic fields created by each wire will more effectively reinforce each other. (C) the net magnetic force on the wires by earth s field is stronger. (D) the magnetic attraction between the wires is stronger. (E) the wires don t fly apart from their magnetic repulsion.. A current loop in a uniform magnetic field will not experience a torque if (A) there is an electric field parallel to the magnetic field. () there is an electric field anti-parallel to the magnetic field. (C) the plane of the current loop is parallel to the magnetic field. (D) the plane of the current loop is parallel to the magnetic field. (E) the magnetic field is not uniform.

5 . The equation: = µ 0 is useful for a circular loop of current when 2a (A) the field point is near the center of the loop. () the field point is anywhere within the plane of the loop. (C) the field point is anywhere on the axis perpendicular to the loop through the loop's center. (D) when the wire is carrying very small currents. (E) when ever the instructor needs it to be. The equation: µ 0 is useful for a finite length of current carrying wire when 2π r (A) when the distance from the wire is much larger than the distances from the ends of the wire. () when the distance from the wire is much smaller than the distances from the ends of the wire. (C) when the wire is carrying very large currents. (D) when the wire is carrying very small currents. (E) when ever the instructor needs it to be. A bar magnet is passed through a coil of wire. The induced current is greatest when (A) the magnet moves quickly, so that it is inside the coil for a short time. () the magnet moves slowly, so that it is inside the coil for a long time. (C) the north pole enters the coil first. (D) the south pole enters the coil first. (E) never (no current is induced since the coil is not moving). N S An electromotive force is induced within a conductor whenever (A) the conductor is in the presence of a magnetic field. () the conductor is in the presence of a changing magnetic field (producing eddy currents, e.g.). (C) the conductor has a component of velocity perpendicular to the magnetic field. (D) the conductor has a component of velocity parallel to the magnetic field. (E) both () and (C) above. Lenz's Law, which characterizes induced currents in terms of a resistance to change in magnetic flux, was characterized by Dr. Gallis as (A) electromagnetic friction. () electromagnetic inertia. (C) electromagnetic pressure. (D) electromagnetic tension. The equation: da = 0 (A) indicates that there is no magnetic field ( = 0). () indicates that there is no magnetic charge (no isolated poles). (C) indicates that superconductivity is occurring. (D) indicates that Gauss's law does not work for magnetic fields.

6 A circular loop of wire is in a region of magnetic field which is uniform and increasing in strength, directed out of the page. (A) There will be an induced current, which circulates clockwise. () There will be an induced current, which circulates counter clockwise. (C) There is insufficient information to determine the direction of the induced current flow. (D) There will not be any induced current. A circular loop of wire is in a region of magnetic field which is uniform, directed into the page and increasing in strength with time,. (A) There will be an induced current which circulates clockwise. () There will be an induced current which circulates counter clockwise. (C) There is insufficient information to determine the direction of the induced current flow. (D) There will not be any induced current. Two circular loops lie one above the other in a vertical stack, as shown. One is connected to a source that supplies an increasing current, while the other is a simple conducting loop. Then (A) the second loop will have an induced current in the same direction as the current in the first loop. () the second loop will have an induced current in the opposite direction as the current in the first loop. (C) the second loop will have an induced current perpendicular to the current in the first loop. (D) the second loop will not have an induced current (E) the second loop will vaporize. Two circular loops lie side by side in the same plane. One is connected to a source that supplies an increasing current, while the other is a simple conducting loop. Then (A) the second loop will have an induced current in the same direction as the current in the first loop. () the second loop will have an induced current in the opposite direction as the current in the first loop. (C) the second loop will have an induced current perpendicular to the current in the first loop. (D) the second loop will not have an induced current (E) the second loop will vaporize.

7 [The same set of answers applies to the following questions] Which of the following is Ampere's law, which allows us to calculate magnetic fields in situations with a great deal of symmetry (such as around a long straight wire)? A displacement current (i.e. a changing electric field) creates a magnetic field : How to create electric fields from changing magnetic flux: There is no magnetic equivalent to electric charge : The Lorentz force law : The Maxwell's Equation that shows how a flow of electric charge can create a magnetic field 9. The Maxwell's Equation that shows how Magnetic Fields can be created by changing Electric Fields. (A) E da = Q encl ε o. () da = 0. (C) F = q(e + v ). (D) d = µ o ( J da + ε o d dt E da). (E) E d = d dt da). All magnetic fields have their origin in (A) iron atoms. () permanent magnets. (C) magnetic domains. (D) moving electric charges. (E) The origin of magnetic fields cannot be characterized in any simple manner. The magnetic field at the center of the circular loop (shown at right) carrying a current clockwise will be directed (A) into the page. () out of the page. (C) clockwise. (D) counterclockwise. (E) there is no magnetic field unless the current is changing.

8 A circular loop of wire is in a region of magnetic field, which is uniform and constant, directed into the page. (A) There will be an induced current which circulates clockwise. () There will be an induced current which circulates counter clockwise. (C) There is insufficient information to determine the direction of the induced current flow. (D) There will not be any induced current.

9 Part Problems A strip of potassium 2.0 cm wide and 1mm thick carrying a current of 100 A produces a Hall emf with magnitude 223 µv in a magnetic field of 5.00 T. (a) What is the density n of free electrons in potassium? (b) What is the magnitude of the drift velocity of the electrons? f the magnetic field is then decreased to 2.50 T, t (c) What is the Hall emf? (d) What is the density n of free electrons in potassium? w Charges are accelerated by an accelerating potential of 80 kv (of appropriate polarity for positive or negative charges) into a region of uniform magnetic field (directed out of the page). f the charges are electrons, Accelerating potential V (A) What is the speed of the electrons as they enter the (parallel plates) magnetic field? () ndicate the path of the electrons on the diagram at right (label the path e). (C) What is the radius of the circular path taken by the electrons as they travel in the uniform magnetic field? f the charges are protons: (D) What is the speed of the protons as they enter the magnetic field? (E) ndicate the path of the protons on the diagram at right (label the path p). (F) What is the radius of the circular path taken by the protons as they travel in the uniform magnetic field? Region of uniform magnetic field

10 A mass spectrometer is constructed as shown by allowing particles to enter a velocity selector (with crossed Electric and Magnetic fields and then entering a region of uniform magnetic field only. The electric field within the velocity selector is 1x10 6 V/m and the magnetic field with both the velocity selector and mass spectrometer is.2t, directed out of the page (see diagram). The ions are deflected by the magnetic field, and traverse a semicircle of radius R, at the end of which they are detected (a) n the figure at right, sketch in the trajectory of the ions within the magnetic field. (b) For both C 12 and C 14 (two isotopes of carbon), calculate the speed v of the ions as they leave the accelerating potential and the radius R of the semicircular trajectories. The masses of C 12 and C 14 are 12u and 14u, respectively, where 1u = 1.66x10-27 Kg. KEEP AT LEAST 3 SGNFCANT FGURES THROUGH OUT THESE CALCULATONS. velocity selector (c) How far apart are the endpoints of the semicircular trajectories? uniform magnetic field The figure is an end view of two long parallel wires perpendicular to the xy plane, each carrying a current, the top is coming out of the page, the bottom is going into the page. (a) On the diagram, show the contributions of to from each wire, and the resultant at the point P (b) Derive an expression for the magnitude of the resultant for any point on the x-axis in terms of the x- coordinate of the point, the y-coordinate of the wire a, and the current. (c) Make a graph of the magnitude of as a function of x. y axis a a x P x axis

11 Two long straight parallel wires carry currents as shown at right. The wires are separated by a distance of.400 m. 1 is 2.00 A and 2 is 4.00 A. (A) What is the magnitude and direction of the net magnetic field half way between the wires? () What is the magnitude and direction of the net magnetic field.200 m to the right 2 1 of 2? The figure below shows two long straight wires each carrying an electric current perpendicular to the page. The current at the origin is 4.00 A. The other current is located on the y-axis at y=3.00m and carries a current of 8.00 A. ) On the figure, sketch the contributions to the magnetic field produced by each wire at the point x=4.00 m. A) Determine the x and y components of the net magnetic field created at the field point located on the x axis at x=4.00 m. The figure is the cross sectional view of a circular current loop of radius a which lies in the yz plane, carrying a current, coming out of the page at the top of the figure and going into the page at the bottom of the figure. (a) On the diagram, show the contributions of to d from a small segment of length ds at the top of the loop and the corresponding piece of wire on the opposite side (i.e. the segment of length ds at the bottom of the loop). Also show the resultant d at the point P due to these two contributions. Symmetry will play a roll! (b) Derive an expression for the magnitude of the resultant d for any point on the x-axis in terms of the x- coordinate of the point, the radius of the of the wire a, the current, and the length of the segment ds starting with the field of a small segment of current carrying wire: µ dl rˆ o y axis y axis d = 2 4π r (c) Find an expression for the magnetic field due to the loop by adding up (integrating) all the ds a segments around the loop. x P x axis z axis

12 A.100 kg,.200 m long conducting bar is attached to a vertical rail to complete a vertical circuit of total resistance 5.00 Ω. The bar is released to drop from the top of the track at t = 0. There is a horizontal magnetic field of.250 T coming out of the page. (A) Use either the changing flux through the circuit (harder) or the motional EMF generated by the moving bar (easier) to relate the induced current in the bar to the downward speed of the bar v. () Determine the bar's "terminal velocity", the speed at which the magnetic force on the current through the bar is equal in magnitude (but opposite in direction direction) to the gravitational force on the bar..2m falling bar v The long straight wire in the figure shown carries a current of 20.0 A. The rectangular loop whose long edges are parallel to the wire carries a current of 8.00 A. The loop is 10 cm long, 4 cm wide and the left side of the loop is located 2 cm from the long straight wire. Find the magnitude and direction of the net magnetic force exerted on the loop by the magnetic field of the wire. = 8 A = 20 A A horizontal square loop of wire of.500 m on a side has 8 turns. t is placed in a vertical magnetic field whose strength varies in time as: =2 3t 1 2 t t 3. A) Determine the flux through the loop as a function of time. ) Determine the induced EMF as a function of time. Now suppose the loop is oriented vertically instead of horizontally: C) Determine the flux through the loop as a function of time. D) Determine the induced EMF as a function of time.

13 A conducting bar moves on conducting rails as shown. There is a uniform magnetic with magnitude.4 tesla directed into the page. The bar is pushed to the right at a constant speed of 25 m/s. The resistance (which completes the loop) is 2 Ω. a) What is the EMF? b) What is the size and direction (clockwise or counter clockwise) of induced current? c) What is the power dissipated in the EMF? d) What is the force on the current due to the magnetic field? R v e) The (mechanical) force which must be applied to keep the bar moving is equal in size (opposite direction) to the magnetic force. Using this information, calculate the mechanical power which must be delivered to keep the bar moving. (recall from physics 201 that P =Fv) A long straight wire is directed as shown, and is steadily increasing at a rate of di dt. a)at a an instant when the current is, what are the magnitude and direction of the magnetic field a distance r to the right of the wire? b) What is the magnetic flux through the narrow strip of width dr indicated in the diagram? c) What is the total flux through the loop? ("add up" all such strips across the loop) d) What is the induced EMF in the loop? i a r dr L All answers should be expressed solely in terms of i, r, a, b, L, di dt, and µ 0 b

14 A flat coil with area.01 m 2 and 50 turns lies in a uniform and constant magnetic field of.100 T. The coil is rotated about an axis through the plane of the loop that is perpendicular to the magnetic field. Thus the angle θ between a line perpendicular to the area and the direction of the magnetic field can be written as θ = ω t. The coil makes 60 rotations per second (recall that ω = 2πf ). The coil and the load resistance have a total resistance of 20 Ω. a) What is magnetic flux through the coil as a function of time? b) What is the EMF induced in the coil as a function of time? c) What is the current in the loop as a function of time? d) What is the magnetic moment of the current in the coil as a function of time? e) What is the magnetic torque on the coil as a function of time? f) What is the power dissipated in the resistance as a function of time? g) What mechanical power must be supplied to maintain the coils constant angular velocity? ω θ = ω t A square loop of wire with resistance R is moved at a constant speed v across a uniform magnetic field confined to a square region whose sides are twice the length of the square loop. (a) n the space provided, graph the magnetic flux through the loop as a function of the position of the loop (referenced to the front of the loop). The maximum flux has been determined for you. (b) n the second space provided make a qualitative graph the induced current as a function of position. (c) Determine the maximum current in terms of, L, v, and R. (this will determine the limits of the second graph. Φ Φ L 2 2L L = 2L v -L 0 L 2L 3L Φ 0 2L -L 0 L 2L 3L 0 -L 0 L 2L 3L

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