Question

A long solenoid has $200$ turns per cm and carries a current of $2.5$Amp. The magnetic field at its centre is (${\mu _0} = 4\pi \times {10^{ - 7}}Wb/{m^2}$​)
$\left( A \right)314 \times {10^{ - 2}}Wb/{m^2}$
$\left( B \right)6.28 \times {10^{ - 2}}Wb/{m^2}$
$\left( C \right)9.42 \times {10^{ - 2}}Wb/{m^2}$
$\left( D \right)12.56 \times {10^{ - 2}}Wb/{m^2}$

Answer 1

Electric field is caused by stationary charges and magnetic field are caused by moving electric charges. Ampere’s circuital law states the relationship between the magnetic and the electric field. Here we are considering a long solenoid. Use the Ampere circuit law to obtain the magnetic field at the centre.

Formula used:
$B = {\mu _0}IN$
${\mu _0}$ is the permeability of the medium, $i$ is the current enclosed by the closed path and $B$ is the magnetic field.

Complete step by step answer:
Ampere’s circuital law states the relationship between the magnetic and the electric field. This law states that the integral of (B) in an imaginary closed path is equal to the product of current enclosed by the closed path and permeability of the medium. The force will be zero, when the conductor is parallel to the magnetic field. The force will be maximum, when it is perpendicular to the magnetic field

Number of turns are wound around a cylinder by using an insulated wire called solenoid.
Here we know that number of turns per length $n = \dfrac{N}{l}$
Here for $1cm$ they have $200$ turns then for $1m$ we will have $200 \times {10^2}$ turns
$B = \dfrac{{{\mu _0}IN}}{L}$
Substitute the values to get the magnetic field,
$B = \dfrac{{4\pi \times {{10}^{ - 7}} \times 200 \times {{10}^2} \times 2.5}}{1}$
Then $B = 6.28 \times {10^{ - 2}}Wb/{m^2}$

Hence, the correct answer is option (B).

Note: A magnetic field is generated, whenever a current travels through a conductor. The force will be zero, when the conductor is parallel to the magnetic field. The force will be maximum, when it is perpendicular to the magnetic field. The Magnetic field lines around a conductor carrying current are concentric circles whose centres lie on the wire. Right-Hand Thumb Rule determines the direction of magnetic field lines.