Asolenoid that is 35 cm long and contains 450 circular coils 2.0 cm in diameter carries a 1.75-a current. (a) what is the magnetic field at the center of the solenoid, 1.0 cm from the coils? (b) suppose we now stretch out the coils to make a very long wire carrying the same current as before. what is the magnetic field 1.0 cm from the wire’s center? is it the same as that in part (a)? why or why not?

Explanation:

a )  No of turns per metre

n = 450 / .35

= 1285.71

Magnetic field inside the solenoid

B = μ₀ n I

Where I is current

B = 4π x 10⁻⁷ x 1285.71 x 1.75

= 28.26 x 10⁻⁴ T

This is the uniform magnetic field inside the solenoid.

b )

Magnetic field around a very long wire at a distance d is given by the expression

B = ( μ₀ /4π ) X 2I / d

= 10⁻⁷ x 2 x ( 1.75 / .01 )

= .35 x 10⁻⁴ T

In the second case magnetic field is much less. It is due to the fact that in the solenoid magnetic field gets multiplied due to increase in the number of turns. In straight coil this does not happen .

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