Question:
A solenoid of length 50 cm and a radius of cross-section
1 cm has 1000 turns of wire wound over it. If the current
carried is 5 A, the magnetic field on its axis, near the
centre of the solenoid is approximately (permeability of
free space $\mu _0=4 \pi \times 10^{-7} T-mA^{-1}) $
A solenoid of length 50 cm and a radius of cross-section
1 cm has 1000 turns of wire wound over it. If the current
carried is 5 A, the magnetic field on its axis, near the
centre of the solenoid is approximately (permeability of
free space $\mu _0=4 \pi \times 10^{-7} T-mA^{-1}) $
Updated On: Jul 6, 2022
- $0.63 \times 10^{-2} T$
- $1.26 \times 10^{-2} T$
- $2.51 \times 10^{-2} T$
- $6.3 \, T $
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The Correct Option is B
Solution and Explanation
The magnetic field is given by
$\hspace15mm B=\mu _0ni $
where $\mu _0=4 \pi \times 10^{-7}T \, mA^{-1}, $
$\hspace15mm n=\frac {1000}{50 \times 10^{-2}},i=5 \, A $
$\therefore \hspace15mm B=4 \pi \times 10^{-7} \times \frac {1000}{50 \times 10^{-2}}\times 5 $
$\hspace15mm B=1.26 \times 10^{-2} 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.