Question

Consider the arrangement of charges in the diagram below.
The distances labeled are all from lines to lines or lines to centers of point charges or centers of point charges to centers of point charges.
What is the magnitude and direction of the electric field at point P in terms of k (the Coulomb constant) and D?

• A. $\frac{15}{D^2}N/C$ downward
• B. $\frac{3}{D^2}N/C$ to the right
• C. $\frac{k}{D^2}N/C$ to the right
• D. $\frac{4k}{D^2}N/C$ to the downward
• E. $0$

Answer 1

The correct option is C $\frac{k}{D^2}N/C$ to the right

Electric field due to charge 1 $E_1=\frac{k\left(16\right)}{(4D{)}^2}=\frac{k}{D^2}$ $N/C$ (upwards)

Electric field due to charge 2 $E_2=\frac{k\left(1\right)}{(D{)}^2}=\frac{k}{D^2}$ $N/C$ (Downwards)

Electric field due to charge 3 $E_3=\frac{k\left(5\right)}{(2D{)}^2}=\frac{5k}{4D^2}$ $N/C$ (Right)

Electric field due to charge 4 $E_4=\frac{k\left(1\right)}{(2D{)}^2}=\frac{k}{4D^2}$ $N/C$ (Left)

Net electric field in vertical direction $E_v=E_1-E_2=0$

Net electric field in horizontal direction $E_H=E_3-E_4=\frac{5k}{4D^2}-\frac{k}{4D^2}=\frac{k}{D^2}$ $N/C$ (to the right)