#### Question

A solenoid 3.142m long and 5.0 cm in diameter has two layers of windings of 500 turns each and carries a current of 5A. Calculate the magnetic induction at its centre along the axis.

#### Solution

Given:

Length of solenoid, l = 3.142m

Diameter, d = 5.0cm = 5 × 10^{-2}m

Radius, r = 2.5cm = 2.5 × 10^{-2}m

No. of turns, N = 2 × 500 = 1000

Current, I = 5A

To calculate:

The magnetic induction at its centre along the axis.

Magnetic Induction, B = ?

Formula:

B = μ_{o}nI

Solution:

`"B"=mu_o("N"/"l")"I"`

`therefore"B"=(4pixx10^-7xx1000xx5)/3.142`

`therefore"B"=2xx10^-3 "T"`

Hence, the magnetic induction at the centre of the circular loop along its axis is 2 × 10^{-3}T.

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#### APPEARS IN

Solution A Solenoid 3.142m Long and 5.0 Cm in Diameter Has Two Layers of Windings of 500 Turns Each and Carries a Current of 5a. Calculate the Magnetic Induction at Its Centre Along the Axis. Concept: Inductance and Capacitance.