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Question 4 (12.5 points) Point charges q1-2 4.0 x 10-6 C are fixed on the x-axis at x -3.0 m and x 3.0 m. What charge q must be placed at the origin so that the electric field vanishes at x-0, y 3.0 m? -8.23*106 c -3.28* 10.6 C -2.83 * 10.6 C -2.38*106 C

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Answer #1

We can solve this by first finding resultant electric field at point on Y-axis due to both the charge on X-axis. And then equate this resultant electric field with the electric field due to the new charge q bought at the origin. If the charge at origin produces same electric field as produced by the resultant of charge Q1 and Q2 but in opposite direction then electric field will vanish.

All working is shown below.

wen S Shoun in aye due to chare E 2: EL-feld due to change V2 ER Resultont Electoic fetd le P。int P (0,9m) VE 2. (o,o) 2. E Electic Siend due to 3 m change 、a/、 トlaced at origin distance b/w ahe。Wu and Folnt Flectme field is give n ng.IE: ‘一2 charge a. and oint p s Same s magnitude IETE but dioection will be dt (36) 2m2 3461 1 N/c Now this e sultont E can he tutn tie chazge nega tive charge and thu a mt beX lo 2-m2 Eis to uward the chaage

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