3. A line of charge is placed on the x axis between x 5.00 m and x 5.00 m. The l

Question

3. A line of charge is placed on the x axis between x 5.00 m and x 5.00 m. The linear charge density is given by 10 AC/cm. Consider a field point on the y-axis, located at y 2.0 m, as shown below. P (x 0, y 2.0 m) a. (2 points) How much charge da is contained in a segment of the wire of length dx? b. (5 points) Charge element da 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 associated with the electric field for this charge element da? (Hint: Your answer should be a function of x and the unit vectors i and j.) d. (5 points) If there is symmetry to the problem, what is the only component of needed s 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", eft", etc.) f. (10 points) Suppose you placed a +10 uC 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. Here,

dq = lambda dx

dq = (-10 uC/cm)dx [ANSWER]

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B.

By Pythagorean theorem,

|r| = sqrt (x^2 + y^2)

As y = 2.0 m,

|r| = sqrt (x^2 + 4.0 m^2) [ANSWER]

where x is in meters.

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C.

The unit vector is

r^ = r / |r|

r^ = [-x i^ + 2.0 m j^] / sqrt (x^2 + 4.0 m^2) [ANSWER]

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D.

There is symmtery.We only need the y components of r, as the x components of the electric fields cancel by symmetry.

Again, we only need the y components. [ANSWER]

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