1. A long straight telephone cable has a charge per unit length of. The cable stretches along thex axis from -a toa. Find the electric field along theyaxis by first drawing a picture of the situation, then following the steps below:

a. What is the expression for the charge elementdq.

b. What direction does the electric field point at any location along the positivey axis? Explain how you know the answer without doing any calculations.

c. What is the electric field generated by this charge element in the direction from part (b) for any arbitrarydq and any arbitrary position on they axis.

d. What are the variables in your equation that can change their value (for a particular location on they axis, say a distanceL from thex axis)?

e. Write all of the above variables in terms of the angular variable.

f. Integrate over alldq's to find the electric field.

g. If you were to redo the problem again, but you were to find the electric field at a location not on they axis, would you get a different answer? Why or why not?

2. Now let the length of the wire be infinite.

a. Using the answer from part (1g), determine what the electric field would be for an infinite length wire (i.e. the value ofa gets very large)?

b. If you were to do part (2a) of this problem again, but you were to find the electric field at a location not on they axis, would you get a different answer? Why or why not?