Question:
A long solenoid has 200 turns per cm and carries a current i. The magnetic field at its centre is 6.28 x$10^{-2}$ 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 x$10^{-2}$ 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
- $1.05\times10^{-2} weber/m^{2}$
- $1.05\times10^{-5} weber/m^{2}$
- $1.05\times10^{-3} weber/m^{2}$
- $1.05\times10^{-4} weber/m^{2}$
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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,
$6.28\times10^{-2}=\mu_{0} \times200 \times10^{2}\times i \ldots\left(i\right)$
$and \, \quad B=\mu_{0} \times100\times10^{2}\times\left(i / 3\right)\ldots$ (ii)
Solving Eqs.(i) and (ii), we get
$B \approx1.05 \times10^{-2} wb / m^{2}$
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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.