In this contour plot you can see lines of equal potential. The lines are labeled

Question

In this contour plot you can see lines of equal potential. The lines are labeled with their potential values in units of Volts. These potential lines are generated by a collection of point charges.

Part 1:
What is the minimum number of point charges that are needed to generate a potential surface like the one shown here?

Part 2:
What is the value of the x-component of the electric field at the blue point with coordinates (-0.9,-2.2) cm? (Hint: you need to extract this value graphically. In order to do this, it helps to draw a straight horizontal line from one equipotential line to another, crossing the point. For your convenience, you can do this in the contour plot above by clicking on the starting point of your line, dragging the mouse, and then releasing at the endpoint. The intial and final coordinates of your line will be displayed below the contour plot. Once drawn, you can move the starting point of the line by using the arrow keys on your keyboard; holding the shift key down at the same time will move the endpoint of the line.)

Part 3:
What is the value of the y-component of the electric field at the same point?

Explanation / Answer

Part 1

Minimum number of point charges that are needed to generate a potential surface like the one shown here is 3. As we can see, there are three separate circular regions which represent one point charge each.

Part 2

At the blue point with coordinates (-0.9,-2.2) cm, V = -1 V and x = -0.9

Thus, x-component of the electric field is,

Ex = V/ x = -1 / 0.9 = -1.111 V/cm = -0.0111 V/m

Part 3

At the blue point with coordinates (-0.9,-2.2) cm, V = -1 V and y = -2.2

Thus, y-component of the electric field is,

Ey = V/ y = -1 / 2.2 = -0.4545 V/cm = -0.004545 V/m

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