Question

A solenoid 2 m long and 3 cm in diameter. It has 5 layers of winding of 1000 turns each and carries a current of 5 A. What is the magnetic field at its centre? How will the magnetic induction change when a core of i) antimony ii) soft iron is introduced inside the solenoid?

Answer 1

$$\begin{gathered} \mathrm{Length}\mathrm{of}\mathrm{solenoid}=2\mathrm{m} \\ \mathrm{Diameter}=3\mathrm{cm}=0.03\mathrm{m} \\ \mathrm{Number}\mathrm{of}\mathrm{turns}\mathrm{per}\mathrm{metre},\mathrm{n}=\frac{5\times 1000}{2}{\mathrm{m}}^{-1} \\ =2500{\mathrm{m}}^{-1} \\ \mathrm{Magnetic}\mathrm{field}\mathrm{is}\mathrm{given}\mathrm{by}, \\ \mathrm{B}={\mathrm{\mu }}_0\mathrm{n}\mathrm{I} \\ =4\mathrm{\pi }\times {10}^{-7}\times 2500\times 5 \\ =1.57\times {10}^{-2}\mathrm{T} \end{gathered}$$
(i) Magnetic induction will decrease.
(ii) Magnetic induction will increase.