Physics 222 2/1/01 name________________________

KE = 1/2 mv², F= ma , v² - v_o² = 2ax, v = v_o - at, x = v_ot+1/2at², a_c=v_T²/r

k = 1/4e_o = 9x10⁹ Nm²/C² m_o = 4p x10^-7 Tm/A

1) A particular DNA molecule has a charge of -230e where e = 1.6x10^-19 C. A class of proteins called histones causes DNA to fold up inside the cell. A histone has a charge of +190e and is located 1.4x10^-10 m from the DNA.

a) What is the force of attraction between the histone and the DNA molecule?

b) What is the electric field at a point exactly half way between the histone and the DNA molecule?

2) An oil droplet of mass 1x10^-14 kg is found to stay motionless, neither falling nor rising, when placed in a uniform electric field of 1.53x10⁵ N/C.

a) If the charge is negative, which direction must the electric field point to support the charge against gravity?

b) What is the charge of the droplet? (This is how Millikan determined the charge of an electron.)

c) How many electrons is this?

3) The orbital magnetic moment of an electron is m = eh/2m = 9.27x10^-24 J/T.

a) If the electron orbiting a hydrogen atom is considered as a current flow of 1.6x10^-3 A, what is the radius of the orbit?

b) If an external magnetic field of 2T is applied, that is the maximum torque on the orbiting electron?

4) A coaxial cable has a wire in the center of radius a = .05 mm carrying current I = 2.2A in one direction while the shielding (a thin metal cylinder centered on the wire of radius b = 0.2 mm) carries a current of 3.1A in the opposite direction. Be sure to indicate the direction of all vectors clearly. Use Ampere's law to find:

a) The magnetic field outside the coaxial cable at any radius;

b) The magnetic field inside the cable for radius r > a but less than the radius of the shielding, b.

5) Normally a coaxial cable has no net charge on it. Suppose, however, that for some reason a line charge of +1µC/m is on the axis of the cable. Assume the current is now zero. Be sure to indicate the direction of all vectors clearly. Using Gauss' Law, find:

a) The electric field outside the coaxial cable at any radius;

b) The electric field inside the cable for radius r > a but less than the radius of the shielding, b.

6) It is known that certain fish can detect magnetic fields. As a hypothesis, suppose the mechanism for this is the magnetic force acting on a collection of charge in the fish brain.

a) If the fish swims at 3 m/s and feels a maximum force of 0.02 N in the earths magnetic field (3x10^-5 T), how large is the charge deposit?

b) Draw a diagram indicating the direction the fish is swimming, the direction of the magnetic field (assume a uniform field) and the direction of the force on the fish. Assume the maximum force case.

c) Based on your above calculations, state why you think the hypothesis about a charge deposit in a fish brain may or may not be correct.

7) a) Given the radius a and the current I, use the Biot Savart law find and expression for the magnetic field at point p.

b) Explain why the leads of the wire don't contribute.

Bonus:

a) What is the difference between resistance and resistivity?

b) What are Kirchoff's rules?

c) Explain how a mass spectrometer works?