A rod of length, L, has total charge, Q, and lies on the x axis (depicted in bol

Question

A rod of length, L, has total charge, Q, and lies on the x axis (depicted in bold) with the left end on the origin. Consider the following to calculate the electric field at a fixed point on the positive x axis that is B units from the origin where B > L. Label each of the elements described above on the diagram below. Given the previous description, identify the following quantities as either a variable or a constant, Again note that the field will only be in the x direction along the axis. But since the distribution is also along the axis, there are no angles to consider. If dq represents the differential for charge and r represents the distance between the fixed point for which potential is calculated and the charged element, find the following. The differential of the magnitude of the electric field for this distribution can be generally written as |dE| = k|kq|/r^2, where we again assume a positive charge. Rewrite dE_x for this charge geometry in terms of the variable, x. dE_x = k dq/r^2 = Set up the definite integral calculating the electric field at a fixed point on B units on the positive x axis. E_x = integral

Explanation / Answer

5)

L constant

B variable

x constatn

W constant

6)

dq = charge per unit * dx

dq = Q/L*dx

so

dq/dx = Q/L

r = B-L+x

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