The ends of a metal bar rest on two horizontal north-south rails. The bar lies east-west. There is a magnetic field directed north. A battery causes the electrons in the bar to drift to the east. The resulting magnetic force on the bar is directed: (A) north (B) south (C) east (D) west (E) vertically

E) Vertically

A charged particle is projected with its initial velocity parallel to a uniform magnetic field. The resulting path is a: (A) spiral (B) parabolic arc (C) circular arc (D) straight line parallel to the field (E) straight line perpendicular to the field

D) Straight line parallel to the field

A proton traveling with speed v enters a uniform electric field directed parallel to the plane of the page. There is also a magnetic force on the proton opposite to the electric force. Which of the following is a possible direction for the magnetic field? (A) downward (B) upward (C) leftward (D) out of the page (E) into the page

D) Out of the page

If e represents the magnitude of the proton charge what minimum magnitude of the magnetic field could balance the electric force on the proton? (A) E/v (B) eE/v (C) vE (D) eE (E) evE

A) E/v

At point X a charged particle has KE of 9 µJ. It follows a path through a region with both electric and magnetic fields and arrives at Y with KE of 11 µJ. What is the work done by the magnetic field on the particle? (A) 11 µJ (B) 2 µJ (C) -2 µJ (D) -11 µJ (E) None of the above

E) None of the above (zero)

In a region of space there is a uniform B field in the plane of the page but no E field. A positively charged particle with velocity v directed into the page is subject to a force F in the plane of the page directed upward. Which vector best represents the direction of B? (A) leftward (B) upper-left (C) upper-right (D) rightward (E) lower-right

E) Lower-right

A negatively charged particle in a uniform magnetic field B moves with constant speed v in a circular path of radius r. Which graph best represents r as a function of the magnitude of B if speed v is constant? (A) linear increase (B) hyperbolic decrease (C) linear increase from origin (D) curve increasing then leveling (E) linear decrease

B) Hyperbolic decrease

Which of the following equations implies that it is impossible to isolate a magnetic pole? (A) ∮E·dA = q/ε₀ (B) ∮E·dl = −dΦ/dt (C) ∮B·dA = 0 (D) ∮B·dl = µ₀i + µ₀ε₀dΦ/dt (E) None of the above

C) ∮B·dA = 0

A square loop of wire 0.3 m on a side carries 2 A of current in a uniform 0.05 T magnetic field. The left side of the loop is on a fixed axis. When the plane of the loop is parallel to the field what is the magnitude of the torque about the axis? (A) 0.00225 Nm (B) 0.0090 Nm (C) 0.278 Nm (D) 1.11 Nm (E) 111 Nm

B) 0.0090 Nm

A uniform magnetic field B is in the +y-direction. A proton initially moves with velocity v in the xy-plane at an angle θ to the y-axis. The proton will subsequently follow what kind of path? (A) straight line in direction of v (B) circular path in xy-plane (C) circular path in yz-plane (D) helical path with axis parallel to y-axis (E) helical path with axis parallel to z-axis

D) Helical path with its axis parallel to the y-axis

A beam of protons moves in the +x-direction through crossed electric and magnetic fields balanced for zero deflection. The magnetic field points in the +y-direction. In what direction must the electric field point? (A) +y (B) +z (C) −x (D) −y (E) −z

E) Negative z-direction

A negatively charged particle in uniform magnetic field B moves in a circular path of radius r. Which graph best depicts how the frequency of revolution f depends on the radius r? (A) constant (B) decreasing curve (C) increasing line (D) decreasing line (E) increasing curve

A) Constant

A particle of charge +e and mass m moves with speed v perpendicular to a uniform magnetic field B directed into the page. The path is a circle of radius r. Which gives the correct direction of motion and equation relating v and r? (A) Clockwise eBr = mv (B) Clockwise eBr = mv² (C) Counterclockwise eBr = mv (D) Counterclockwise eBr = mv² (E) Counterclockwise eBr² = mv²

C) Counterclockwise eBr = mv

The period of revolution of a particle of charge +e and mass m moving in a uniform magnetic field B is: (A) mr/eB (B) √(m/eB) (C) 2πm/eB (D) 2π√(m/eB) (E) 2π√(mr/eB)

C) 2πm/eB

A charged particle can move with constant velocity through a region containing both an electric field and a magnetic field only if the: (A) E field is parallel to B field (B) E field is perpendicular to B field (C) E field is parallel to velocity (D) B field is parallel to velocity (E) B field is perpendicular to velocity

B) Electric field is perpendicular to the magnetic field

A square loop of wire carrying current I is in the plane of the page in a uniform magnetic field B pointing toward the bottom of the page. Which shows the correct initial rotation of the loop? (A) A (B) B (C) C (D) D (E) E

C) C

A copper sheet causes electrons to drift toward the bottom of the page. The sheet is in a magnetic field B directed into the page. P1 is on the left edge and P2 is on the right edge. Which is true? (A) P1 is at higher potential than P2 (B) P2 is at higher potential than P1 (C) P1 and P2 are at equal positive potential (D) P1 and P2 are at equal negative potential (E) Current will cease to flow

B) P2 is at higher potential than P1

Two long parallel wires carry currents I1 and I2 with attractive force magnitude F. What currents give an attractive force of 4F? (A) 2I1 and ½I2 (B) I1 and ¼I2 (C) ½I1 and ½I2 (D) 2I1 and 2I2 (E) 4I1 and 4I2

D) 2I1 and 2I2

A solid cylindrical conductor of radius R carries current I uniformly distributed throughout its interior. Which graph best represents magnetic field intensity B as a function of radial distance r from the axis? (A) A (B) B (C) C (D) D (E) E

A) A

A long solenoid of length l radius r N turns carries current I and has field B0. A solenoid with the same N l and I but radius 2r would have magnetic field magnitude: (A) B0/4 (B) B0/2 (C) B0 (D) 2B0 (E) 4B0

C) B0

Two very long parallel wires carry equal currents in the same direction into the page. At point P equidistant (10 cm) from each wire the magnetic field is: (A) zero (B) into the page (C) out of the page (D) to the left (E) to the right

E) Directed to the right

A current I is uniformly distributed over the cross section of a long cylindrical conductor of radius a. Which graph best represents B as a function of distance r from the axis? (A) A (B) B (C) C (D) D (E) E

E) E

Two long parallel wires each carry current i into the page separated by distance d. The force on the right wire due to the left wire is directed: (A) to the right (B) to the left (C) upward (D) downward (E) into the page

B) To the left

Two parallel wires carrying current i separated by distance d have force per unit length F0. The wires are moved to separation 2d and current increased to 2i. The new force per unit length is: (A) F0/4 (B) F0/2 (C) F0 (D) 2F0 (E) 4F0

D) 2F0

Two identical parallel conducting rings with a common axis carry equal currents I in opposite directions separated by distance a. At point P (center of the left ring) the magnetic field due to both currents is: (A) zero (B) in the plane perpendicular to the x-axis (C) in the +x-direction (D) in the −x-direction (E) none of the above

C) Directed in the positive x-direction

A cross section of a long solenoid carrying current I is shown. All of the following statements about the magnetic field B inside the solenoid are correct EXCEPT: (A) B is directed to the left (B) an approximate value for B may be determined using Ampere's law (C) the magnitude of B is proportional to current I (D) the magnitude of B is proportional to turns per unit length (E) the magnitude of B is proportional to the distance from the axis

E) The magnitude of B is proportional to the distance from the axis

Two long parallel wires are a distance 2a apart. Point P is in the plane of the wires and a distance a from wire X. With current I in wire X only the field at P is B0. With equal currents I in the same direction in both wires the magnitude of the field at P is: (A) 2B0/3 (B) B0 (C) 10B0/9 (D) 4B0/3 (E) 2B0

D) 4B0/3

A narrow beam of protons produces a current of 1.6 x 10⁻³ A. There are 10⁹ protons per meter along the beam. Which is the best estimate of the average speed of the protons? (A) 10⁻¹⁵ m/s (B) 10⁻¹² m/s (C) 10⁻⁷ m/s (D) 10⁷ m/s (E) 10¹² m/s

D) 10⁷ m/s

Which of the following describes the lines of magnetic field in the vicinity of the proton beam? (A) concentric circles around the beam (B) parallel to the beam (C) radial and toward the beam (D) radial and away from the beam (E) there is no magnetic field

A) Concentric circles around the beam

A rigid rectangular wire loop ABCD carrying current I1 lies in the plane of the page above a very long wire carrying current I2. The net force on the loop is: (A) toward the wire (B) away from the wire (C) toward the left (D) toward the right (E) zero

A) Toward the wire

In which of the following cases does there exist a nonzero magnetic field that can be conveniently determined by using Ampere's law? (A) outside a point charge at rest (B) inside a stationary cylinder carrying uniformly distributed charge (C) inside a very long current-carrying solenoid (D) at the center of a current-carrying loop of wire (E) outside a square current-carrying loop of wire

C) Inside a very long current-carrying solenoid

A wire of radius R has current I uniformly distributed across its cross-sectional area. Ampere's law is used with a concentric circular path of radius r where r < R. Which equation results from a correct application of Ampere's law? (A) B(2πr) = µ0I (B) B(2πr) = µ0I(r²/R²) (C) B(2πr) = 0 (D) B(2πR) = µ0I (E) B(2πR) = µ0I(r²/R²)

B) B(2πr) = µ0I(r²/R²)

Two parallel wires each carrying current I repel each other with force F. If both currents are doubled the force of repulsion is: (A) 2F (B) 2√2 F (C) 4F (D) 4√2 F (E) 8F

C) 4F

The currents in three parallel wires X Y and Z each have magnitude I. X and Z point downward and Y points upward. Wire Y is closer to wire X than to wire Z. The magnetic force on wire Y is: (A) zero (B) into the page (C) out of the page (D) toward the bottom of the page (E) toward the left

E) Toward the left