Use Coulomb\'s law to determine the magnitude of the electric field at points A

Question

Use Coulomb's law to determine the magnitude of the electric field at points A and B in (Figure 1) due to the two positive charges (Q = 5.9 mu C) shown. Suppose that a = 5.1 cm. Determine the magnitude of the electric field at A. Express your answer to two significant figures and include the appropriate units. E_A = Determine the angle between the direction of the electric field at point A and the positive x-direction. Express your answer using two significant figures. Determine the magnitude of the electric field at point B. Express your answer to two significant figures and include the appropriate units. Determine the angle between the direction of the electric field at point B and the positive x-direction. Express your answer using two significant figures.

Explanation / Answer

a) The point A is located in mid of two positive charges,

distanc ebetween charges and point A = sqroot (4a^2 + a^2) = sqroot (5a^2)= a sqroot(5)

angle = tan^-1 ( a/2a) = 26.565 degree apprx

Ea( electric field at A) = 2 (9 x 10^9 ) (5.9 x 10^-6) / (5a^2) sin 26.565

plugging a= 5.1 cm, 5a^2=0.013 m

Ea = 8169.23 x 10^ 3 sin 26.565= 3653..384 N/C apprx

b) angle will be 90 degree

c)Eb

Ex ( x componet of electric field at B) = 9 x 10^9 (5.9 x 10^-6 ) cos 45/ (2a^2) - 9 x 10^9 ( 5.9 x 10^-6) cos 18.43 / (10a^2) = 53.1 x 10^ 3 ( 135.98 - 36.389) = 5283 N/C

Ey = 9 x 10^9 (5.9 x 10^-6 ) sin 45/ (2a^2) + 9 x 10^9 ( 5.9 x 10^-6) sin18.43 / (10a^2)

= 7866.205 N/C

Eb = sqroot (5283^2+ 7866.205^2) = 9475.614N/C

d) tan^-1 ( Ey/Ex) = 56.11 degree apprx

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