In this exercise you will figure out the equipotential point/points(s)/line/surf

Question

In this exercise you will figure out the equipotential point/points(s)/line/surface in the xy plane where V = 0 for two point charges of charge q and -2q found respectively at (x,y,z) = (-1,0,0) and (x,y,z) = (1,0,0), and draw the result on Fig. ??.

(a) Given that V is a scalar, equipotentials generally form surfaces in three di- mensions. This contrasts with the electric field, where we found only one position where it was zero for a pair of point charges. In the x-y plane for the two charges shown, do we expect a point, two points or a line where V = 0?

(b) Make a guess where the potential should be zero. Should it be zero closer to the smaller or larger charge? Why?

(c) Assign a label (x,y) to a general point in the x-y plane

In this exercise you will figure out the equipotential point/points(s)/line/surface in the xy plane where V = 0 for two point charges of charge q and -2q found respectively at (x,y,z) = (-1,0,0) and (x,y,z) = (1,0,0), and draw the result on Fig. ??. Given that V is a scalar, equipotentials generally form surfaces in three di- mensions. This contrasts with the electric field, where we found only one position where it was zero for a pair of point charges. In the x-y plane for the two charges shown, do we expect a point, two points or a line where V = 0? Make a guess where the potential should be zero. Should it be zero closer to the smaller or larger charge? Why? Assign a label (x,y) to a general point in the x-y plane-placing a point on off the x-axis can help in writing a general equation. Write an equation to solve summing the potential expected at this arbitrary point (x,y) from each of the charges. Set this potential equal to 0. Simplify and solve the equation to find a quadratic equation in two variables. Interpret your result: Create a table of results (x,y) that solve your equation. Solve for the value of x when y = 0, and the value of y when x = -1, then plot your results on the above graph. Draw a smooth curve through your points, putting in more points if you are not confident about the shape of the equipotential. Draw electric field lines on the above diagram. Pay special attention to how they cross the equipotential line.

Explanation / Answer

a) at x=-2l potential is zero, so it's a point in xy plane

b)it should be closer to the smaller charge (2q) because potential is directly proportional to the amount of charge and in versely proportional to the distance, thus for same q/r ratio , for smaller charge r should be small

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.