Assignment #15

Section 28-1 & 28-2

Date Due: Wed. Oct. 29

Magnetic Force on a Freely Moving Charge

5. At one particular moment a 270 gram particle with a charge q = -8.90 mC {+3.67 mC} is moving vertically upwards at a speed v = 32.3 m/s in a uniform magnetic field B = 7.80 T.

(A) If the B-field is horizontal and pointing due East {South}, determine the magnitude and direction of the force that the magnetic field will exert on the particle at that moment. Describe the particle's subsequent motion.
Ans:{F = 925 mN, due East. As viewed from the south the particle is moving clockwise in a vertical circle with a radius of 305 m.}

(B) If the B-field is vertical, pointing straight up, determine the magnitude and direction of the force that the magnetic field will exert on the particle at that moment. Describe the particle's subsequent motion. Ans:{?}

(C) If the B-field is horizontal and pointing at an angle of 34.0^o South of due East {S of W}, determine the magnitude and direction of the particle's acceleration at that moment. Describe the particle's subsequent motion.
Ans:{a = 3.42 m/s², 56.0^o S of E in the horizontal plane. Particle is moving in a vertical circle with a radius of 305 m and whose axis is pointing at 34.0^o S of W}

(D) If the B-field is pointing upwards at an angle of 41.0^o {66.0^o} above the horizon directed towards the North {East}, determine the magnitude and direction of the force that the magnetic field will exert on the particle at that moment. Describe the particle's subsequent motion.
Ans:{F = 376 mN, due North. Particle will move in a helix whose axis is along the direction of the magnetic field with a radius of 124 m. The particle will be moving at 29.5 m/s along the direction of the B-field}

Assignment #16

Section 28-1

Date Due: Fri. Oct. 31

Magnetic Force on a Current Carring Wire

16. A horizontal wire carrying a current of 4.75 A {6.50 A} has a length of 170 cm {25.0 cm}. The current runs from North to South {West to East}. The wire is placed in a constant magnetic field .

(A) If the B-field has a magnitude of 32.0 mT and is straight up, what is the magnitude and direction of the force on the wire? Ans:{52.0 mN, due South}

(B) If the B-field has a magnitude of 147 G and is due North, what is the magnitude and direction of the force on the wire? Ans:{23.9 mN, straight up}

(C) If the B-field has a magnitude of 11.0 mT and makes an angle of 30.0^o with the horizontal plane, directed upwards from due South, what is the magnitude and direction of the force on the wire? Ans:{17.9 mN, downward at 60.0^o from due South}

(D) If the B-field has a magnitude of 8.60 kG and makes an angle of 30.0^o with the horizontal plane, directed upwards towards due East, what is the magnitude and direction of the force on the wire? Ans:{699 mN, due South}

BONUS:

(E) What is the direction of the B-field if a 32.0 mT B-field it exerts a vertical upward force of 12.0 mN {34.0 mN} on the wire? Ans:{40.8^o or 139.2^o N of E in the horizontal plane}

Assignment #17

Section 28-4

Date Due: Mon. Nov. 3

Hall Effect

17. A metallic strip that is 0.240 mm thick and 1.50 cm {1.20 cm} tall carries a current of 18.0 A down the length of the strip. When a 1.10 T {2.20 T} magnetic field is applied horizontally to the vertical face of the strip, a Hall potential difference of 16.0 mV is measured across the height of the strip.

(A) What is the magnitude of the electric vertical field across the height of the strip due to the Hall voltage? Ans:{1.33 mN/C}

(B) What is the drift velocity of the current down the strip? Ans:{0.606 mm/s}

(C) What is the density of charge carriers down the strip? Ans:{6.44x10²⁸ #/m ³}

(D) What is the magnitude of the magnetic force on a charge carrier (an electron) moving down the strip? Ans:{2.13x10^-22 N}

BONUS:

(E) When the vertical surface of the strip is rotated by an angle q with respect to the magnetic field and the Hall voltage drops to 11.0 mV. Through what angle was the strip rotated?

Assignment #18

Section 29-2

Date Due: Tue. Nov. 4

Creation of Magnetic Field

18. Two long horizontal parallel wires carry currents of I₁ = 12.0 Amps {5.00 Amps} and I₂ = 23.0 Amps {2.00 Amps} in the same direction, due West {North}. The wires are 75.0 cm apart, and the wire I₁ is south {west} of the second wire.

(A) What is the magnitude and direction of the magnetic field B half way between the two wires? Ans:{ B₁ = 2.67 mT down, B₂ = 1.07 mT up, B_T = 1.60 mT down}

(B) What is the magnitude and direction of the magnetic field 13.0 cm to the north {45.0 cm to the east} of I₂ in the horizontal plane? Ans:{ B₁ = .833 mT down, B₂ = .888 mT down, B_T = 1.72 mT down}

(C) Where in space will the magnetic field be equal to zero, i.e., were will the magnetic field of the two wires cancel each other? Ans:{directly between the wires, 53.6 cm to the east of wire I₁}

(D) What is the magnitude and direction of the force per unit length that wire I₁ exerts on wire I₂? Ans:{2.67 mN/m due West}

BONUS:

(E) What is the magnitude and direction of the magnetic field B at a point that 26.0 cm directly above the wire I₂?
Ans:{ B₁ = 1.26 mT at -70.9^o, B₂ = 1.54 mT horizontal, B = 2.29 mT, at -31.4^o, towards East}

Assignment #19

Section 30-2

Date Due: Wed. Nov. 5

Magnetic Flux through a Loop and Induced EMF

19. A thin square coil, 14.0 cm on a side, is lying in the horizontal plane. The coil has 1520 turns and a total resistance of 250 W. A magnetic field, pointing at an angle of 69.0⁰ above the horizontal plane, is "turned on" in such a way that the B-field increases according to B(t) = B_o(1- e ^-t/t) where B_o = 130 G and t = 128 ms { B(t) = a t² where a = 4.40 T/s²}.

(A) What is the flux through the coil of wire 53.0 ms after the field is turned on? Ans:{.344 Wb}

(B) What is the rate at which the flux is changing with time, 53.0 ms after the field is turned on? Ans:{13.0 Wb/s}

(C) What is the direction and magnitude of the flow of current in the coil 53.0 ms after the magnetic field is turned on? State the direction as clockwise or counter clockwise as viewed from above. Ans:{51.9 mA, direction =? }

(D) When will the current in the coil have a magnitude of 2.80 mA {73.0 mA}? Ans:{74.6 ms}

Bonus:

(E) What is the maximum value of the current in the coil?

Assignment #20

Section 30-3 & 30-4

Date Due: Fri. Nov. 7

Motional EMF

20. A conducting rod with a resistance of 6.40 W and a length of 11.0 cm slides along two horizontal, frictionless, conducting rails that have negligible electrical resistance. There is a uniform magnetic field of 23.0 T that is pointed upward at 48.0^o relative to horizontal. The rod is pulled to the right at a constant velocity of 1.20 m/s {41.0 cm/s} by an applied constant force, F_app.

(A) What is the induced emf generated due to the rod’s motion? Ans:{771 mV}

(B) What is the magnitude and direction of the current flow in the rod? Ans:{120 mA, 2 to 1}

(C) What is the magnitude and direction of the magnetic force acting on the rod? What is the magnitude of the applied force, F_app? Ans:{ F_B = 305 mN, 138^o relative to due east; F_app = 226 mN}

(D) Calculate the energy dissipated in the resistor (from P = IV ) during the time it takes the rod to move 7.90 cm? Ans:{17.9 mJ}

BONUS:

(E) Calculate mechanical work done by the applied force (from W = F d ) that it takes to move the rod 7.90 cm to show that it is the same as the energy dissipated in D. Ans:{17.9 mJ}