Download WH HW06

Phys122: Homework Assignment #6
Due: Friday, March 4, by 11 am
Show all your work for full credit:. State the problem, draw diagrams, and always write the
formulas in notation form before you substitute numbers. Show all your steps as you are solving the
problem. And never forget to include units. This is physics, units matter! If you are having difficulty
with any of the problems, ask for help.
1. (4 points) The electric field along the axis of a ring-shaped charge of total charge Q distributed
uniformly is given by E = Qx/(4π0 (x2 + a2 ))3/2 where a is the radius of the ring and x is the
distance from the center of the ring. The electric field at the center of the ring is zero and at
great distances from the ring approaches zero. At what position is the electric field a maximum
for positive values of x?
2. (4 points) Two charges Q1 = −3µC and Q2 = +3µC are located on the y-axis at y1 = -5 cm
and y2 = +5 cm respectively. A third charge Q3 = +24µC is added on the y-axis so that the
electric field at the origin is equal to zero. What is the position of Q3 ?
3. (4 points) A long, thin rod parallel to the y-axis is located at x = - 1 cm and carries a uniform
positive charge density λ = 1 nC/m . A second long, thin rod parallel to the z-axis is located at
x = +1 cm and carries a uniform negative charge density λ = - 1 nC/m. What is the electric
field at the origin?
4. (3 points) If the earth’s electric field is 100 N/C downward, what must be the charge on a 1-kg
object so that it would be ”weightless”?
5. (4 points) An electric field is set up between two parallel plates, each of area 2.0 m2 , by putting
1.0 µC charge on one plate and a -1.0 µC charge on the other. The plates are separated by 4.0
mm. What is the magnitude of the electric field between the plates at a distance of 1.0 mm from
the positive plate?
6. (4 points) A ring 0.71 m in radius carries a charge of + 580 nC uniformly distributed over it.
A point charge Q is placed at the center of the ring. The electric field is equal to zero at field
point P, which is on the axis of the ring, and 0.73 m from its center. What is the charge Q?
7. (2 points, extra credit) Charge Q is uniformly distributed along a thin, flexible rod of length L.
The rod is then bent into the semicircle with radius R. Find an expression for the electric field
~ at the center of the semicircle.
E