# Ch23 Homework Solutions

23.17. Three equal positive charges q are at the corners of an equilaeral triangle of side a, as shown in Figure P23.17.

(a) Assume that the three charges together creat an electric field. Find the location of a point (other than at infinity) where the electric field is zero. (Hint: Sketch the field lines in the plane of the charges.)

(b) What are the magnitude and direction of the electric field at P due to the two charges at the base?

(a) Assume that the three charges together creat an electric field. Find the location of a point (other than at infinity) where the electric field is zero. (Hint: Sketch the field lines in the plane of the charges.)

By symmetry, the field is zero at the center of the triangle.

Use of symmetry is important!

(b) What are the magnitude and direction of the electric field at P due to the two charges at the base?

First, an associated, numerical problem:

Three point charges are located at the corners of an equilateral triangle as in Figure P23.17. Calculate the net electric force on the 7.0 microCoulomb charge.

Sometime, some people consider it easier to solve numerical problems compared to symbolic problems. Typically, tho', symbols are easier to solve than numbers. Now, let's go on with the question as stated.

What are the magnitude and direction of the electric field at P due to the two charges at the base?

(b) What are the magnitude and direction of the electric field at P due to the two charges at the base?

Due to the charge on the left, there is an electric field El that has a magnitude of

El = k q / a2

Due to the charge on the right, there is an electric field Erl that has a magnitude of

Er = k q / a2

The total or net electric field is the vector sum of these these two electric fields,

Which directions do these individual electric field vectors point? Make good diagrams!

Enet,x = 0

Enet,y = Enet

Enet,y = El,y + Er,y

Enet,y = 2 [ k q / a2 ] sin 60o

Enet,y = 2 [ k q / a2 ] (0.866)

Enet,y = 1.732 [ k q / a2 ]

Enet = 1.732 [ k q / a2 ]

pointing in the y-direction.