A long solenoid is formed by winding 70 turns/cm. If 2.0 A current flows, then the magnetic field produced inside the solenoid is:
Show Hint
The formula \( B = \mu_0 n I \) is key for solenoids. Always convert \( n \) into turns/m (SI unit) before substituting.
\(88 \times 10^{-4} T\)
\(123.2 \times 10^{-4} T\)
\(352 \times 10^{-4} T\)
- \(176 \times 10^{-4} T\)
The Correct Option is D
Solution and Explanation
The magnetic field inside a long solenoid is given by:
\[ B = \mu_0 n I \]
where:
- \(\mu_0\) = \(4\pi \times 10^{-7}\) \(\text{Tm/A}\) (permeability of free space),
- \( n = \frac{70}{\text{cm}} = 70 \times 10^2 \, \text{turns/m}, \)
- \( I = 2.0 \, \text{A} \) (current).
Substitute the values:
\[ B = (4\pi \times 10^{-7}) \cdot (70 \times 10^2) \cdot 2 \]
\[ B = 176 \times 10^{-4} \, \text{T} \]
Thus, the magnetic field produced inside the solenoid is \( 176 \times 10^{-4} \, \text{T} \).
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Concepts Used:
Moving Charges and Magnetism
Moving charges generate an electric field and the rate of flow of charge is known as current. This is the basic concept in Electrostatics. Another important concept related to moving electric charges is the magnetic effect of current. Magnetism is caused by the current.
Magnetism:
- The relationship between a Moving Charge and Magnetism is that Magnetism is produced by the movement of charges.
- And Magnetism is a property that is displayed by Magnets and produced by moving charges, which results in objects being attracted or pushed away.
Magnetic Field:
Region in space around a magnet where the Magnet has its Magnetic effect is called the Magnetic field of the Magnet. Let us suppose that there is a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them can be written as,
F = q [ E (r) + v × B (r)] ≡ EElectric +Fmagnetic
This force was based on the extensive experiments of Ampere and others. It is called the Lorentz force.