Physics 114 Exam II 1999

 

Answer each of the following 4 questions and each of the following 4 problems. Each question is worth 10 points each and each problem is worth 15 points.  Be sure to show all your work.

 

Questions

 

1.      An electron is moving in a constant electric field parallel to the x axis.  At the origin, its speed is 2 x 106 m/s and at x = 2 cm its speed is 4 x 106 m/s.  (a) Is the electron's potential energy in the electric field increasing or decreasing.  (b) Is it moving towards a point of higher or lower electric potential?

2       Consider two charged conducting spheres of radii, r1 and r2 where r2 > r1.  The two spheres are connected by a long wire and are at equilibrium.  Compare the following quantities of one sphere to the other.  Determine on which sphere each quantity is greater (or if it is equal on each sphere) and explain why. (a) The electric potential at the surface of the spheres, (b)The electric field at the surface of the spheres (c)The total charge on the surface, (d) The surface charge density

 


3  There are four identical bulbs wired as shown below.  Suppose bulb A in the circuit shown is unscrewed from its socket. (a) How do the brightnesses of the three remaining bulbs change? (b) How do these brightnesses compare with each other?


4  A charged particle having a certain kinetic energy enters a static magnetic field. If no other forces act on the particle while it is within the field, it has the same kinetic energy on leaving the field. Why?

 


Problems

 

1.      For the system of capacitors shown below, find (a) the equivalent capacitance of the system, (b) the potential across each capacitor, (c) the charge on each capacitor and (d) the total energy stored by the group.  The battery has an emf of 90 V, the top two capacitors have capacitance of 3 and 6 mF, and the bottom two capacitors have capacitance of 2 and 4 mF.

 

 

 

 

 

 

 

 

 

 


2.     

In the circuit shown below, use Kirchoffs’ laws to find three unknowns: the current in the resistor R, the value of the unknown emf, e, and the resistance R.

3.      A circular loop of N = 100 turns has a radius of 0.1 m and carries a current of 1.5 A.  The loop is placed in a vertical magnetic field (pointing upward), B = 1 T so that its normal makes an angle of 45o with the horizontal.  (a) What is the magnetic moment of the loop?  (b) What is the initial magnitude of the torque on the loop? (c) What is the maximum torque that this field can exert on the loop?

4.      A cylindrical conductor of radius R = 2.50 cm carries a current of I = 2.50 A along its length; this current is uniformly distributed throughout the cross section of the conductor.  (a) Use ampere's law (clearly showing each step) to calculate the magnetic field midway along the radius of the wire (that is at r = R/2).  (b) Use ampere's law (clearly show your work) to calculate the magnetic field at some distance r, where r >R.  (c)  Find the distance beyond the surface of the conductor at which the magnitude of the magnetic field has he same value as the magnitude of the field at r = R/2.