Question

A uniform continuous line charge with net positive charge Q and length L lies on the x-axis from −L2 to +L2. This problem asks about the electric field at a point on the +y-axis: (0,a). continuous line charge

(1) What is the direction of the x-component of the electric field at (0,a)?

(A) +x(to the right)
(B) -x (to the left)
(C) zero (there is no net horizontal component of the E-field)

Answer 1

The x-component of the electric field at point (0,a) due to a uniform continuous line charge on the x-axis is zero, due to the symmetrical distribution of charge and corresponding cancellation of horizontal electric field components.

Step-by-step explanation:

The student is asking about the direction of the electric field at a point on the positive y-axis due to a uniform continuous line charge distributed along the x-axis. To find the direction of the x-component of the electric field at the point (0,a), we can consider the symmetry of the charge distribution. For any small element of charge on the positive side of the x-axis, there is an identical element of charge on the negative side at the same distance from the origin. The electric fields produced by these two elements at point (0,a) on the y-axis will have the same magnitude but opposite x-components. These x-components will cancel each other out, resulting in a net x-component of the electric field being zero. Therefore, the correct answer to the student's question is (C) zero (there is no net horizontal component of the electric field).

Answer 2

(C) zero (there is no net horizontal component of the E-field)

Step-by-step explanation:

If we subdivide the bar into small pieces, each piece (dx) contains a charge (dq), the electric field of each piece is equivalent to the field of a punctual electric charge, and has a direction as shown in the attached figure. For each piece (dx) in the negative axis there is another symmetric piece (dx) in the positive axis, and as we see in the figure for symmetry the sum of their electric fields gives a resultant in the Y axis (because its components in X are cancelled by symmetry).

Then the resultant of the electric field will be only in Y.

(C) zero (there is no net horizontal component of the E-field)