Consider a line of charge of length L having total charge Q with uniform charge density as shown in the figure below. (A) Consider the electric field at a point P on the horizontal x-axis a distance r from the end of the line of charge as shown above. What direction does the electric field point? Briefly explain your answer. (B) Just from thinking about it (without too much calculation), what do you think the electric field should be (approximately) when r ≫ L? Briefly explain your thinking. (C) Now do a calculation to find an expression for the electric field at the point P. (D) Compare your answer to (C) in the limit where r ≫ L with your answer from (B). Do they agree? (They should!)

Consider a line of charge of length L having total charge Q with uniform charge density as shown in the figure below. (A) Consider the electric field at a point P on the horizontal x-axis a distance r from the end of the line of charge as shown above. What direction does the electric field point? Briefly explain your answer. (B) Just from thinking about it (without too much calculation), what do you think the electric field should be (approximately) when r ≫ L? Briefly explain your thinking. (C) Now do a calculation to find an expression for the electric field at the point P. (D) Compare your answer to (C) in the limit where r ≫ L with your answer from (B). Do they agree? (They should!)

Image text
Consider a line of charge of length L having total charge Q with uniform charge density as shown in the figure below. (A) Consider the electric field at a point P on the horizontal x -axis a distance r from the end of the line of charge as shown above. What direction does the electric field point? Briefly explain your answer. (B) Just from thinking about it (without too much calculation), what do you think the electric field should be (approximately) when r L? Briefly explain your thinking. (C) Now do a calculation to find an expression for the electric field at the point P . (D) Compare your answer to (C) in the limit where r L with your answer from (B). Do they agree? (They should!)

Detailed Answer