Question

In: Physics

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

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?

Expert Solution

(a) How much charge dq is contained in a segment of the wire of length dx?

. The linear charge density is -10 microcoulomb per cm, then we can write it as:

(b) 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.)

As the field point is located at y: - 2 m, then we can write the expression for r as:

(c) 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)

The unit vector can be written as:

(d) 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”.

As there is symmetry with respect to he Y axis, the y component is the one necessary:

genius_generous answered 6 months ago

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