PHY 132 Second Midterm Solutions, 4/02

 

 

 

1. Three parallel wires carry currents as indicated on the Figure, with I1=2.00A and I2=5.00A and d=1.00cm.  Calculate the magnitude of the magnetic force on the topmost wire.

 

There are two forces acting on this wire, in opposite directions. Use F/L=m0 I I'/ 2pr, where I=5A, and the distance r is either 1cm or 2cm with corresponding currents of 2A and 5A.  The net force is  m0(5A) (2A) / 2p (0.01m) - m0 (5A) (5A) / 2p (0.02m) = 2x10-7 x (1000 - 1250) = -5x10-5N.  The magnitude of the force is 5.00x10-5N.

 

2. A beam of electrons is under the simultaneous influence of an electric field E=3.94x105V/m and a magnetic field of 4.62x10-2T. The fields are perpendicular to the beam and to each other.

The beam is not deflected (remains straight).  What will be the radius of the orbit if the electric field is removed?  (Hint: first calculate the speed of the electrons in the beam.)

 

The speed is determined by qvB=qE resulting in v=E/B=8.53x106m/s.  The radius of the orbit is R=mv/qB=mE/qB2=1.05x10-3m=1.05mm.

 

3. What is the magnitude of the current in the  10 W resistor in the Figure?

 

Pick currents, loops and use Kichoff's laws (see Figure).  The junction rule yields I3=I1+I2. For the upper loop:  10-2I1-10I3=0; lower loop: 10-4I2-10I3=0.  Eliminate I3, and solve for I1and I2 to obtain I1=0.588A and I2=0.294A.  Therefore I3 = 0.882A

 

4. The answer is C, 2.4V clockwise

 

 

5 A 300W resistor is in series with a 0.250H inductor and a 8.00mF capacitor. What is the impedance of the circuit at an angular frequency of 500rad/s?

 

A 20.6W

B 325W

C  425W

D 480W

E 550W

F none of the above

 

The impedance is  Z=[R2 + (wL -1/wC)2]1/2, where wL=125W,  1/wC= 2501W.  The result is

Z=325W

6. Four resistors and a battery of negligible internal resistance are assembled to make the circuit in the Figure. The electromotive force is 4.5V, the resistances are R1=2.50W, R2=3.75W, R3=9.50W and R4=6.25W. Find the current in the battery.

 

A 1.03A

B 1.80A

C 1.48A

D 1.00A

E 0.98A

F none of the above

 

The circuit is made of  three parallel resistors, in series with the R1=2.50W. The replacement resistor for the three is determined by 1/R'= 1/R2+1/R3+1/R4 = 0.5139 1/W. The total resistance is 4.38W, and the current is 1.03A.