Question

a solenoid is 2.0m long and 3.0m in diameter. it has 5 layers of windows of 1000 turns each and carries of 5.0 A what is the magnetic field at its centre given u=4π*10​

Answer 1

GiveN :

• Length of solenoid (L) = 2 m
• Diameter = 3 m
• No. of turns (N) = 1000 * 5 = 5000
• Current (I) = 5 A

To FinD :

• Magnetic field at centre of solenoid

SolutioN :

Formula for magnetic field at centre of solenoid is :

$\large{\underline{\boxed{\tt{B\ =\ \mu_0 nI}}}}$

Where,

• B = Magnetic Field
• $\mu_0$ = permeability of free space
• n = Number of turns per unit length
• I = Current

$\\\\ \longrightarrow{\tt{B\ =\ \mu_0 \dfrac{N}{L} I}} \\\\\\ \longrightarrow{\tt{B\ =\ 4\ \pi \times\ 10^{-7} \times\ \dfrac{N}{L}\ \times\ I }} \\\\\\ \longrightarrow \tt{4\ \pi \times\ 10^{-7}\ \times\ \dfrac{5000}{2}\ \times\ 5 } \\\\\\ \longrightarrow \tt{B\ =\ 4\ \pi \times\ 10^{-7}\ \times\ 2500\ \times\ 5} \\\\\\ \longrightarrow \tt{B\ =\ 12500\ \times\ 4\ \pi \times\ 10^{-7}} \\\\\\ \longrightarrow {\boxed{\tt{B\ =\ 50000 \pi\ \times\ 10^{-7}\ T}}}$

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Where,

$\;\;\;\;\;\;\; \bullet \:\: \tt{\mu_0\ =\ 4 \pi\ \times\ 10^{-7}}$

$\\\ \;\;\;\;\;\; \bullet \:\: \tt{ n\ =\ \dfrac{N}{L}}$