Problem 3 (a) Students prepares cards, matching the level curves (equipotential

Question

Problem 3 (a) Students prepares cards, matching the level curves (equipotential lines) with the corresponding potentials. They made the cards for the gravitational equipotential lines for a binary star and for the electrostatic equipotential lines for a dipole. They mix up the cards, help them to match them back. (b) Refer to the equal probability lines for the bivariate normal distribution. Let points A and B be equidistant from the origin Yet these points are clearly not on the same probability level line. Which of them lies on a higher probability level line? See the illustrations on the following pages.

Explanation / Answer

3a) First cotour plot is for binary star potential and second contour plot is for electric dipole potential. Since in first figure both objects have same colour in the plot they have equal potential. For gravitational force mass is always positive. While in second graph both objects have different colours therefore they have opposite charges.

3b) Since the distribution is narrower on x axis as compared to y axis, point having less x value as compared to other will have more probability.

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