Question:
A long solenoid has $200$ turns per cm and carries a current $i$. The magnetic field at its centre is $6.28 \times 10^{-2}$ weber/$m^2$. Another long solenoid has 100 turns per cm and it carries a current $i/3$. The value of the magnetic field at its centre is:
A long solenoid has $200$ turns per cm and carries a current $i$. The magnetic field at its centre is $6.28 \times 10^{-2}$ weber/$m^2$. Another long solenoid has 100 turns per cm and it carries a current $i/3$. The value of the magnetic field at its centre is:
Updated On: Jul 5, 2022
- $1.05 \times 10^{-2}$ weber/$m^2$
- $1.05 \times 10^{-5}$ weber/$m^2$
- $1.05 \times 10^{-3}$ weber/$m^2$
- $1.05 \times 10^{-4}$ weber/$m^2$
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The Correct Option is A
Solution and Explanation
Magnetic field due to a long solenoid is given by
$B=\mu\,_{0}ni$
From given data,
$6.28\times10^{-2}=\mu_{0}\times 200\times10^{2}\times i ...\left(i\right)$
and $B=\mu_{0} \times 100\times10^{2} \times\left(i/3\right)...\left(ii\right)$
Solving Eqs.(i) and (ii), we get
$B\approx1.05\times10^{-2}\,Wb/m^{2}$
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Concepts Used:
Moving Charges and Magnetism
Moving charges generate an electric field and the rate of flow of charge is known as current. This is the basic concept in Electrostatics. Another important concept related to moving electric charges is the magnetic effect of current. Magnetism is caused by the current.
Magnetism:
- The relationship between a Moving Charge and Magnetism is that Magnetism is produced by the movement of charges.
- And Magnetism is a property that is displayed by Magnets and produced by moving charges, which results in objects being attracted or pushed away.
Magnetic Field:
Region in space around a magnet where the Magnet has its Magnetic effect is called the Magnetic field of the Magnet. Let us suppose that there is a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them can be written as,
F = q [ E (r) + v × B (r)] ≡ EElectric +Fmagnetic
This force was based on the extensive experiments of Ampere and others. It is called the Lorentz force.