A line of charge is placed on the x-axis between x = -5 m and x= 5 m . The linear charge density is -10 microcoulomb per cm .Consider a field point on the y-axis, located at y - 2.0 m.
a. (2 points) How much charge dq is contained in a segment ofthe wire of length dx?
b. (5 points) Charge element dq is located at the point (x, 0).What is the distance r from the charge element to the field point?(Hint: Your answer should be a function of x.)
c. (5 points) What is the unit vector r hat associated with theelectric field for this charge element dq? (Hint: Your answershould be a function of x and the unit vectors i hat and j hat)
d. (5 points) If there is symmetry to the problem, what is theonly component of r hat needed (is not zero after integration)? Ifthere is no symmetry that can be exploited, say “no symmetry”.
e. (20 points) What is the electric field vector at the fieldpoint? (Use the Cartesian unit vectors in your answer for E; do notsimply say “up”, “left”, etc.)
f. (10 points) Suppose you placed a +10 microcoulomb charge atthe field point. Would it be attracted toward the x-axis, pushedaway from the x-axis, or neither? What is the magnitude of theforce acting upon it?
