A long solenoid has 200 turns per cm and carries a current of 2.5 Amp. The mag. field at its cen

step 1 For the solenoid magnetic field at center, I can write the value of b is equal to mu not and i.

A long solenoid has 200 turns per cm and carries a current...

A long solenoid has 200 turns per $\mathrm{cm}$ and carries a current of $2.5 \mathrm{Amp}$. The mag. field at its centre is tesla.
(a) $\pi \times 10^{-2}$
(b) $2 \pi \times 10^{-2}$
(c) $3 \pi \times 10^{-2}$
(d) $4 \pi \times 10^{-2}$

Key Concepts

Permeability of Free Space

The permeability of free space (denoted ??) is a physical constant that characterizes the ability of a vacuum to support magnetic field lines. It is a key parameter in the equations deriving magnetic fields in various scenarios, including inside a solenoid, and its value is defined in the SI system.

Units Conversion

Consistency in units is crucial when using formulas in physics. In the context of solenoids, the number of turns per unit length must be converted into standard SI units (turns per meter) if provided in another unit (such as turns per centimeter). Failure to perform proper unit conversion can lead to incorrect calculations.

Ampere’s Law

Ampere’s Law is a fundamental principle in electromagnetism which states that the line integral of the magnetic field around a closed loop is proportional to the electric current passing through the loop. Applying this law to a solenoid leads to the derivation of the formula for the magnetic field inside the solenoid.

Magnetic Field of a Solenoid

This concept involves understanding that the magnetic field inside a long solenoid is uniform and can be calculated using the formula B = ?? n I, where B is the magnetic field, ?? is the permeability of free space, n is the number of turns per unit length (in turns per meter), and I is the current. This formula is derived from Ampere’s Law under the assumption that the solenoid is long enough that edge effects are negligible.

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