PhysicsLAB: 2000 C2 E&M

Three particles, A, B, and C, have equal positive charges Q and are held in place at the vertices of an equilateral triangle with sides of length

, as shown in the figure below. The dotted lines represent the bisectors for each side. The base of the triangle lies on the x-axis, and the altitude of the triangle lies on the y-axis.

	i. Point P₁, the intersection of the three bisectors, locates the geometric center of the triangle and is one point where the electric field is zero. On Figure 1, draw the electric field vectors E_A, E_B, and E_C at P₁ due to each of these charges. Be sure your arrows are drawn to reflect the relative magnitude of the fields.

	ii. Another point where the electric field is zero is point P₂ at (0,y₂). On Figure 2, draw electric field vectors E_A, E_B, and E_C at P₂ due to each of the three point charges. Also indicate in the chart below whether the magnitude of each of these vectors is greater than, less than, or the same as for point P₁.

	(b) Explain why the x-component of the total electric field is zero at any point on the y-axis.

	(c) Write a general expression for the electric potential V at any point on the y-axis inside the triangle in terms of Q, , and y.

	(d) Describe how the answer to part (c) could be used to determine the y-coordinates of points P₁ and P₂ at which the electric field is zero. (You do not need to actually determine these coordinates.)