### How far away is the milky way from our nearest neighbor

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Q. Our galaxy, the Milky Way, contains approximately 4.0 x 10^11 stars with an average mass of 2.0 x 1030 kg each. How far away is the Milky Way from our nearest neighbor, the Andromeda Galaxy, if Andromeda contains roughly the same number of stars and attracts the Milky Way with a gravitational force of 2.4 x 10^30 N

Q. A solid cylindrical conducting shell of inner radius a = 5.1 cm and outer radius b = 7.1 cm has its axis aligned with the z-axis as shown. It carries a uniformly distributed current I2 = 6.4 A in the positive z-direction. An inifinte conducting wire is located along the z-axis and carries a current I1 = 4 A in the negative z-direction.

What is the integral from s to p of B dot dL, where the integral is taken along the dotted path shown, first from point P to point R at (x,y) = (0.707d, 0.707d), and then to point S at (x,y) = (0.6d, 0.6d)?

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