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Three different problems of a vortex penetrating a superconducting thin film have been addressed. It has been shown that the flux coupled from a vortex into a pickup loop or SQUID washer can be obtained from knowledge of the current distributions which flow in the absence of a vortex, a much easier calculation. Results are given for the case of the SQUID washer. The current distribution for a vortex near a circular hole in a film has been found in the strong shielding limit, and the force on the vortex deduced. The current distribution of a Josephson vortex penetrating a planar junction, such as a bicrystal junction, has been calculated. The form of the Josephson vortex is different from that usually assumed, with a long range tail. The size of the Josephson vortex is typically a factor of two larger than that obtained by taking the conventional expression in terms of the Josephson penetration depth.