prob5.30 4 for where Q and Q2 are the charges on the particles and r is the sepa

Question

prob5.30

4 for where Q and Q2 are the charges on the particles and r is the separatin between them. The quantity 4TEo is constant, Show that the electrostatie force is conservative. obtain an expression for the potential energy. Problem 5.30 A particle is subjected to a force given by (a) Prove that this force is conservative. (b) obtain an expression for the potential energy. Problem 5.31 Newton's law of universal gravitation states that the force between two particles of masses mi and m2 is Gmim2 where G a constant and r is the distance between the particles. Use is this force to obtain the gravitational potential energy of the system, expression zero of potential Select an appropriate point for the

Explanation / Answer

5.3 ) F = M i + N j

for force to be conservative

del M/del y = del N/del x

so ,

del (2x + y) / del y = 1

del (x + 2y) / del x = 1

Both are equal , so the force is conservative

b) U = integral(F) dx dy

= -K ( x^2 + xy) i + (xy + y^2) j)

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