Question:
A solenoid $1.5\, m$ long and $0.4\, cm$ in diameter possesses $10$ turns per cm length. A current of $5\, A$ flows through it. The magnetic field at the axis inside the solenoid is
A solenoid $1.5\, m$ long and $0.4\, cm$ in diameter possesses $10$ turns per cm length. A current of $5\, A$ flows through it. The magnetic field at the axis inside the solenoid is
Updated On: Apr 18, 2024
- $2\pi \times10 ^{-3}T$
- $2\pi \times 10 ^{-5}T$
- $4\pi \times 10 ^{-2}T$
- $4\pi \times 10 ^{-3}T$
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The Correct Option is A
Solution and Explanation
Magnetic field at the axis inside the solenoid
$B = \mu_{0}\, ni $
Here, $n = 10$ tums/cm =$ 1000 $ turns/m, $i = 5\, A $
$B = 4\pi \times10^{-7} \times1000 \times5 $
$ = 2\pi \times10 ^{-3} \, T$
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.