a) What are the strength and direction of the electric field at the position ind

Question

a) What are the strength and direction of the electric field at the position indicated by the dot in the figure(Figure 1)? (

Give your answer in component form. Assume that x-axis is horisontal and points to the right, and y-axis points upward.

Express your answers using two significant figures separated by a comma.)

b) What is the magnitude of the electric field at the position indicated by the dot in the figure.

(Express your answer using two significant figures.)

Explanation / Answer

Field of +10nC = 9*10^9*10*10^-9/0.03^2 = 10^5N/C and in vector form, -10^5N/C j

Similarly, Field of -5nC = 9*10^9*5*10^-9/0.05^2 = 10^5N/C and in vector form, 1.8*10^4N/C i

Distance between -10nC and the dot = (0.05^2+0.03^2)^1/2 = 0.0583m and field due to this charge will be along this line joining the 2 points, which is inclined at tan^-1(0.03/0.05) = 30.96 degrees with x axis

So, Field of -10nC = 9*10^9*10*10^-9/0.0583^2 = 2.6479*10^4N/C and in vector form, 2.6479*10^4N/C * cos 30.96 i + 2.6479*10^4N/C * sin 30.96 j = 2.2706*10^4 N/C i + 1.3621*10^4 N/C j

So, strength and direction of the electric field at the position indicated by the dot in the figure(Figure 1) is -10^5N/C j + 1.8*10^4N/C i + 2.2706*10^4 N/C i + 1.3621*10^4 N/C j = 4.0706*10^4 N/C i - 8.6378*10^4 N/C j , towards tan^-1(- 8.6378*10^4 /4.0706*10^4) = 295.23 degrees from x axis

and using two significant figures, 41000 i - 86000 j N/C , 300

magnitude of the electric field at the position indicated by the dot in the figure = ((4.0706*10^4)^2 + (8.6378*10^4)^2)^1/2 = 95488.938 N/C and answer using two significant figures is 95000 N/C

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