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What is a solenoid? Why do we usually keep its diameter small in comparison to its length?

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If a conducting wire (coated with an insulating paint or varnish) is closely wound on a (long) cylindrical core, the resulting coil is referred to as solenoid. It is usual to keep the diameter of the solenoid small compared to its length. This is done to bring about a greater degree of uniformity (and simplicity) in the axial magnetic field of the solenoid. 

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