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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)

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Answer:

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

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)

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