i need helps on these Question#1 Question#2 Two point charges are placed at two

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i need helps on these

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Question#2

Two point charges are placed at two of the corners of a triangle as shown in the figure. Find the magnitude and the direction of the electric field at the third corner of the triangle. Please include a multiplication sign (*) to indicate that two units are being multiplied. E= [Num] [Units] at [Num] [Units] counterclockwise from the base of the triangle Two uniformly charged insulating rods are bent in a semicircular shape with radius r = 13.5 cm . If they are positioned so that they form a circle but do not touch and if they have opposite charges of +5.29 mu C and -5.29 mu C , find the magnitude and direction of the electric field at the center of the composite circular charge configuration. Please include a multiplication sign (*) to indicate that two units are being multiplied. E = [Num] [Units] toward the charged rod.

Explanation / Answer

Number 1...

Apply E = kq/r^2

For the -10.9 uC charge

E = (9 X 10^9)(10.9 X 10^-6)/(.13)^2

E = 5.80 X 10^6 N/C upward

For the 15.9 uC charge

E = (9 X 10^9)(15.9 X 10^-6)/(.245)^2

E = 2.38 X 10^6 N/C to the left

Combine the E fields by vector addition using the pythagorean theorem

Net E field = sqrt[(5.80 X 10^6)^2 + (2.38 X 10^6)^2]

E = 6.28 X 10^6 N/C

The direction is found using the tangent function

tan(angle) = 5.8 X 10^6/2.38 X 10^6

angle = 67.7 degrees in the second quadrant

From the base of the triangle, that is 90 + 67.7 = 157.7 degrees

Thus, in summary, the answer is

E = 6.28 X 10^6 N/C at 157.7 degrees counterclockwise from the base of the triangle

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