What speed would a proton need to achieve in order to circle Earth 1000.0 km above the magnetic equator? Assume that Earth’s magnetic field is everywhere perpendicular to the path of the proton and that Earth’s magnetic field has an intensity of 4.00 × 10-8 T.

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Question

What speed would a proton need to achieve in order to circle Earth 1000.0 km above the magnetic equator? Assume that Earth’s magnetic field is everywhere perpendicular to the path of the proton and that Earth’s magnetic field has an intensity of 4.00 × 10^-8 T. (Hint: The magnetic force exerted on the proton is equal to the centripetal force, and the speed needed by the proton is its tangential speed. Remember that the radius of the circular orbit should also include the radius of Earth. Ignore relativistic effects.)

Definition Definition Force on a body along the radial direction. Centripetal force is responsible for the circular motion of a body. The magnitude of centripetal force is given by F C = m v 2 r m = mass of the body in the circular motion v = tangential velocity of the body r = radius of the circular path

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