please answer and explain July 20, 2015s Summer 2015 PHYS 112 Midterm exam 1 (9:

Question

please answer and explain

July 20, 2015s Summer 2015 PHYS 112 Midterm exam 1 (9:00-10:00 am) Tour chargs are aranged at the cormers of a square as show. Four charges are arranged at the corners of a square as shown in the figure. Qi is at L2, L2) Q is at (1/2, L/2). point 's is at the origin. The charges are Q-Q.-20, and Q-+30 Assume that Voll and U-0 at infinity Q1 (A-1 l points) Find the sign (%) and magnitude of charge Q. such that the electric potential at point 'b' is zero. Your answer should be in the form Qu-...) Q. where (..)is a number

Explanation / Answer

given,

Q1 = Q

Q2 = -2Q

Q3 = 3Q

electric potential due to point charge = kQ / r

electric potential ar b due to Q2 = k * -2Q / (L/2)

electric potential ar b due to Q2 = -4kQ / L

let charge og Q4 = c

electric potential ar b due to Q4 = k * c / (L/2)

electric potential ar b due to Q4 = 2kc / L

electric potential ar b due to Q1 = k * Q / (L^2 + (L/2)^2)

electric potential ar b due to Q1 = 2kQ / (L * sqrt(5))

electric potential ar b due to Q3 = k * 3Q / (L^2 + (L/2)^2)

electric potential ar b due to Q3 = 6kQ / (L * sqrt(5))

electric potential at point b is 0

so,

-4kQ / L + 2kc / L + 2kQ / (L * sqrt(5)) + 6kQ / (L * sqrt(5)) = 0

k/L * (-4Q + 2c + 2Q / sqrt(5) + 6Q / sqrt(5)) = 0

-4Q + 2c + 2Q / sqrt(5) + 6Q / sqrt(5) = 0

-4Q + 2c + 8Q / sqrt(5) = 0

2c = 4Q - 8Q / sqrt(5)

c = 0.211Q or

Q4 = 0.211Q

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