A line of charge is placed on the x-axis between x = -5 m and x = 5 m . The line

Question

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 of the 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 the electric field for this charge element dq? (Hint: Your answer should 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 the only component of r hat needed (is not zero after integration)? If there is no symmetry that can be exploited, say “no symmetry”.

e. (20 points) What is the electric field vector at the field point? (Use the Cartesian unit vectors in your answer for E; do not simply say “up”, “left”, etc.)

f. (10 points) Suppose you placed a +10 microcoulomb charge at the field point. Would it be attracted toward the x-axis, pushed away from the x-axis, or neither? What is the magnitude of the force acting upon it?

Explanation / Answer

a)

charge density = - 10 uC/cm = - 1000 uC/m

dq/dx = charge density = -1000

so dq = -1000 dx

b)

using pythagoren theorem

r = sqrt(y2 + x2)

y = -2

r = sqrt(4 + x2)

d)

only component of r^ is in y-direction toward origin

e)

upward since rod is negatively charged

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