Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A=10\, cm ^{2}$ and length $=20\, cm$. If one of the solenoid has $300$ turns and the other $400$ turns, their mutual inductance is $\left(\mu_{0}=4 \pi \times^{-7} Tm A^{-1}\right)$
- $2.4 \pi \times10^{-5} H$
- $4.8 \pi \times10^{-4} H$
- $4.8 \pi \times10^{-5} H$
- $2.4 \pi \times10^{-4} H$
The Correct Option is D
Solution and Explanation
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Concepts Used:
Inductance
Inductance is a key parameter in electrical and electronic circuit designs. Like resistance and capacitance, it is a basic electrical measurement that affects all circuits to some degree.
Inductance is used in many areas of electrical and electronic systems and circuits. The electronic components can be in a variety of forms and may be called by a variety of names: coils, inductors, chokes, transformers, . . . Each of these may also have a variety of different variants: with and without cores and the core materials may be of different types.
There are two ways in which inductance is used:
- Self-inductance: Self-inductance is the property of a circuit, often a coil, whereby a change in current causes a change in voltage in that circuit due to the magnetic effect of caused by the current flow. It can be seen that self-inductance applies to a single circuit - in other words it is an inductance, typically within a single coil. This effect is used in single coils or chokes.
- Mutual-inductance: Mutual inductance is an inductive effect where a change in current in one circuit causes a change in voltage across a second circuit as a result of a magnetic field that links both circuits. This effect is used in transformers.