PHYSCS 22 Fall 2010 - MDTERM #3 SHOW ALL WORK & REASONNG FOR FULL PONTS Question 1. (5 pts): Accurately show or state the direction of the force that is felt by the following charges or currents. +q -q -q Force on wire =? Force on +q =? Force on wire =? Question 2 (5 pts): An electron moes initially with elocity ( 500 iˆ) m/s in a uniform magnetic field ( 1.6 ˆj 1.2kˆ) T. a) (4 pts) What is the magnitude and direction of the acceleration of the electron? b) (1 pt) As clearly as possible, describe what would change if the electron was replaced by a proton, moing with the same speed. (No calculations are necessary)
PHYSCS 22 Fall 2010 - MDTERM #3 Page 2 Question 3. (2 pts): What two things can be found using Ampere s Law, dl o encl? Question 4. (5 pts): An ammeter consists of a pioted coil galanometer of resistance R g and a shunt resistor R s. A current of 0.0115 A through the coil produces a full-scale deflection. The alue of R g = 8.50 and the alue of R s can be changed as needed. You want the ammeter to hae a full-scale deflection when 0.200 A enters it. Show how to find what alue is needed for the shunt resistance, and calculate it. Ammeter R g R s Question 5. (2 pts): How are Lenz s Law and Faraday s Law related to each other?
PHYSCS 22 Fall 2010 - MDTERM #3 Page 3 Question 6. (10 pts): Find the magnetic field at all locations for a long, straight conducting cable, consisting of an inner cylinder carrying current 2, and a cylindrical shell outside the cylinder that carries a total current, as shown. There is a ery, ery thin layer of insulator (that we cannot see) that keeps the inner and outer currents separate. 2 a 2a
PHYSCS 22 Fall 2010 - MDTERM #3 Page 4 Question 7. (4 pts): Show clearly the direction of any induced current in each of the following listed objects, in the gien situation shown below. coil coil loop loop = 0 N S = 0 Constant current flows in the large coil, small coil is at rest into page, loop moing to the right Loop rotates from this position, in the direction shown Question 8. (6 pts): A circular coil of 75 loops, each of radius 12.5 cm, is in a uniform magnetic field that is directed out of the page and perpendicular to the coil. The magnetic field strength aries with time: (t) = (0.0550t 0.0025 t 2 ). What is the current in the loop at time t = 10.0s, gien that its resistance is 30.0? Also, in what direction does the current flow at time t = 10.0s? out
PHYSCS 22 Fall 2010 - MDTERM #3 Page 5 Question 9. (10 pts) An initially uncharged 2.00 F capacitor is placed in series with a 9.00 V battery and a 15.0 resistor. (Remember, show your work/reasoning.) a) (2 pts) What is the final charge on the capacitor (after waiting a long time)? b) (3 pts) At what time will the capacitor be charged to 1/3 of its final charge? c) (2 pts) What is the potential difference oer the resistor when the capacitor is 1/3 charged? d) (1 pt) How much energy does the capacitor store when it is fully charged? e) (2 pts) Explain where the energy stored by the capacitor comes from in this situation.
PHYSCS 22 Fall 2010 - MDTERM #3 Page 6 Question 10. (10pts): An electron is fired at 120,000 m/s as shown, parallel to a current of 20 A and in a uniform electric field of 20,000 N/C, as shown. t is seen to follow a straight, horizontal path. a) (2 pts) ndicate the direction the current flows in the wire. b) (6 pts) Calculate how far from the wire the electron must be for it to moe with constant elocity. E d wire c) (2 pts) The electron is now fired at a slower speed (but still in the same direction and at the same distance from the wire). Explain what (if anything) will change about its motion.
PHYSCS 22 Fall 2010 - MDTERM #3 Page 7 Question 11. (10 pts): (5 pts) You are stranded on an island where the Earth s magnetic field is 4.50 x 10-5 T and parallel to the ground. You take a 176 m long length of wire and loop it into a coil made of circular loops, each of radius 35.0 cm. To recharge your cell phone, you must generate a oltage of 4.75 V. At what minimum angular speed (radians per second) must you rotate the coil? How many reolutions per second is that? (f = / 2 ) (1 pt) s this a reasonable rotation rate? (Why or why not?) (2 pts) Explain if it would make any difference to the rotation rate that is needed if the loops of the coil were made with twice the radius from the same length of wire. (2 pts) What are the most likely reasons that electricity-generating power plants are more easily able to generate higher oltages?
PHYSCS 22 Fall 2010 - MDTERM #3 Page 8 Question 12. (7 pts): A 32.5 cm long solenoid with 750 circular turns has a current of 12.0 A running through it. A proton is fired into the solenoid through a small hole in its bottom, and then emerges exactly 90 relatie to its entry point, as shown. Side iew End iew R=3.00 mm Draw on both pictures aboe. At what speed must the proton hae entered the solenoid? 13. (4 pts): Show clearly the way the current-carrying loops below would tend to rotate, gien their rotational axis and the external magnetic fields they are in. out (Loop seen edge-on)
PHYSCS 22 Fall 2010 - MDTERM #3 Page 9 FORMULAE: F e = E pt = kq/r 2 F = qe V = - E dx V = U/q V pt = kq/r U pts = kq 1 q 2 /r W = q V F = m 2 /r E cap = (Q/A)/ o E fringe = (s/2r)(q/a)/ o E E/K in dielectric E dipole (along axis) = 2sqk/d 3 E dipole (perp to axis) = sqk/d 3 V = R 1/R eq = 1/R 1 + 1/R 2 + R eq = R 1 + R 2 + R = L/ A C = Q/ V 1/C eq = 1/C 1 + 1/C 2 + C eq = C 1 + C 2 + U cap = ½ Q V q = Q(1-e -t/rc ) or q = Qe -t/rc = o e -t/rc or o (1-e -t/rc ) = o + at x = o t + ½ at 2 2 = 2 o + 2a x = ( o /4 )qsin r 2 d = ( o /4 ) dl sin r 2 wire = o /2 r 2 o loop a 2 2 3/ 2 2( x a ) = NA cos solenoid = o n toroid = o N/2 r (F/L) two long wires = o1 2 r 2 F = L x F = q x F = ma = - d /dt or / t C = A x = i (A y z A z y ) + j (A z x A x z ) + k (A x y A y x ) C = A sin CONSTANTS: m e = 9.11 x 10-31 kg m p = 1.67 x 10-27 kg e = 1.60 x 10-19 C c = 3.00 x 10 8 m/s g = 9.8 m/s 2 1 ev = 1.6 x 10-19 J k = 8.99 x 10 9 Nm 2 /C 2 o = 8.85 x 10-12 C 2 /Nm 2 o = 4 x 10-7 Tm/A A circle = r 2