Three charges, each of , are arranged at three of the corners of a 20-nm square

Question

Three charges, each of , are arranged at three of the corners of a 20-nm square as shown in the attached figure. The magnitude of the electric field at D, the fourth corner of the square, is approximately

A.1.4X10^7N/C

B.7X10^6N/C

C.3.6X10^10N/C

D.9X10^6N/C

The direction of the resultant field in the previous problem is

A. in the x-direction B. in the y-direction
C. along the line from the upper-left corner and the point D
D. along the line to the upper-left corner and from the point D
E. none of these is correct

Explanation / Answer

D.9X10^6N/C Assuming D is upper left conner of square: Starting A lower left B lower right C upper right Given: 20 nanometers = 2.0 × 10-8 meters k = 9 * 10 ^ 9 q = 3.2 * 10 ^ -19 C r = 2*10 ^ -8 m Ea = k * q / r ^ 2 =7200000 N/C @ 90 degrees rb = 2.828*10^-8 Eb = k * q / r ^ 2 =3600000 N/C @ 135 degrees r = 2*10 ^ -8 m Ec = k * q / r ^ 2 =7200000 N/C @ 180 degrees sum Ex: 7200000* Cos(90)+ 3600000* Cos(135)+ 7200000* Cos(180) =-9745584.412 N/C sum Ey: 7200000* Sin(90)+ 3600000* Sin(135)+ 7200000* Sin(180) =9745584.413 N/C Angle with the positive x-axis: =135. degrees

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