A point charge of 3.0 $ \mu$C is located on the y-axis at y = 4.0 m,and another point charge of 6.0 $ \mu$C is located on the x-axis at x = 5.0 m.What is the direction (ccw from x axis)of the electric field at (5.0 m,4.0 m)?
A) 72$^{\circ}$
B) 18$^{\circ}$
C) 25$^{\circ}$
D) 53$^{\circ}$
E) 34$^{\circ}$

Question

Quizplus · Accepted Answer

The electric field due to the charge at y = 4.0 m is in the -x direction, and the electric field due to the charge at x = 5.0 m is in the -y direction. The net electric field is therefore in the fourth quadrant, and its direction is given by:$$	an	heta = \frac{E_y}{E_x} = \frac{k(6.0 \mu C)/(5.0 	ext{ m})^2}{k(3.0 \mu C)/(4.0 	ext{ m})^2} = \frac{3}{4}$$$$	heta = 	an^{-1}\left(\frac{3}{4}ight) = 36.9^\circ$$The direction of the electric field is therefore 36.9° counterclockwise from the x-axis.

A Point Charge of 3 μ \muμ C Is Located on the Y-Axis at Y = 4

A Point Charge of 3 $\mu$ C Is Located on the Y-Axis at Y = 4