When a wire of length L is struck broadside by an electromagnetic pulse, the current at the centre of the wire is independent of L during the initial period of time t≤;L/2c. The current behaviour in this initial period is related by a linear convolution integral equation to the incident pulse. Using Laplace transform techniques the large time behaviour of the current is derived. In practice this is very useful since the large time approximation is valid when a/c, where a is wire radius, and for thin wires a/c is very small indeed compared to pulse duration. On this basis, simple approximations to the current waveform are obtained, involving only the incident E-field value V(t), its integral and first moment The various approximations are compared to previously published numerically exact solutions and observed to be very satisfactory. Finally a comparison with experimental data is made.