The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to \(1.2 \times 10^{–5}\). What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?
\(1.2 \times 10^{–5}\)
\(1.2 \times 10^{–3}\)
\(1.8 \times 10^{–3}\)
\(2.4 \times 10^{–5}\)
The Correct Option is A
Solution and Explanation
\(\vec{B'}\)=\(µ0(1-X)ni\) in the material
\(\vec{B}\)=µ0\(ni\) without material
So, fractional increase is
\(\frac{B'-B}{B} =X =1.2 × 10^{-5}\)
So, the correct option is (A): \(1.2 \times 10^{–5}\)
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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.