Question

A solenoid 10.0 cm in diameter and 64.6 cm long is made from copper wire of diameter 0.100 cm, with very thin insulation. The wire is wound onto a cardboard tube in a single layer, with adjacent turns touching each other. What power must be delivered to the solenoid if it is to produce a field of 7.10 mT at its center?

_____W

Answer 1

As the adjacent turns are touching each other, so total number of turns is

  

So, total number of turns per unit length is

Magnetic field due to a solenoid at its center is given by

  

Where,

And I is current in the wire

Putting all the values, we get

  

Given the diameter of the solenoid is 10.0 cm or 0.1 m . So the length of the wire in one turn is

  

So, total length of the wire is

Area of the cross section of the wire is

  

Resistivity of copper is 1.72 x 10^-8 .

So, the resistance of the solenoid is

  

Therefore, the total power needed by the solenoid is

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