Arectangular loop of wire with side lengths a and b lies in the first quadrant of the ry plane with one corner at the origin. the side along the r-axis has length a. a nonunifornm magnetic field b(y, t) =-ky3t2ż + k~5t2x, where k is a positive constant. (a) find the magnetic flux through the loop as a function of time (b) find the emf induced in the rectangular loop. (c) will the current resulting from the induced emf flow clockwise or anti-clockwise when viewed from a point in space with z > 0?

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.

Distance^2= yellow line ^2 (see picture) = 30^2 + 49^2so distance = squareroot of (300^2 +49^2)i dont know if this is how to solve it, but i cnt think of another way

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