The magnetic field lines inside a current carrying long solenoid are in the form of
parallel straight lines
Understanding the behavior of magnetic fields created by current-carrying conductors is a fundamental concept in electromagnetism. One important device that generates a magnetic field in a controlled way is a solenoid.
What is a Solenoid?
A solenoid is essentially a coil of wire wound in the shape of a cylinder. When an electric current passes through the wire of the solenoid, it produces a magnetic field both inside and outside the coil.
Magnetic Field of a Long Solenoid
The question specifically asks about the magnetic field lines inside a current-carrying long solenoid. A "long solenoid" is one where the length of the solenoid is much greater than its diameter.
For a long solenoid, the magnetic field has distinct characteristics:
- Inside the solenoid: The magnetic field is strong and remarkably uniform throughout the volume inside the solenoid, except near the ends.
- Outside the solenoid: The magnetic field is very weak compared to the field inside. For an ideal, infinitely long solenoid, the magnetic field outside is practically zero.
Shape of Magnetic Field Lines Inside a Long Solenoid
Magnetic field lines are visual representations of the magnetic field. Their density indicates the strength of the field, and their direction at any point gives the direction of the field. For a uniform magnetic field, the field lines have specific properties:
- They are parallel to each other.
- They are equally spaced.
Because the magnetic field is uniform inside a long solenoid (away from the ends), the magnetic field lines inside are parallel and equally spaced.
Let's consider the options provided for the shape of the magnetic field lines inside a current-carrying long solenoid:
- ellipse: Elliptical field lines are typically associated with dipole fields or fields around loops, but not the uniform field inside a long solenoid.
- parabola: Parabolic field lines are not characteristic of the field inside a solenoid.
- hyperbola: Hyperbolic field lines are also not characteristic of the field inside a solenoid.
- parallel straight lines: This shape represents a uniform magnetic field, which is exactly what exists inside a long solenoid, away from its ends.
Therefore, the magnetic field lines inside a current carrying long solenoid are in the form of parallel straight lines.
Revision Table: Magnetic Field Patterns
| Source | Shape of Field Lines (General) | Field Strength Pattern |
|---|---|---|
| Single straight wire | Concentric circles around wire | Decreases with distance from wire |
| Circular loop | Concentrated and roughly uniform at center, diverging outside | Strongest at center, weaker further away |
| Bar Magnet | Closed loops emerging from North pole and entering South pole | Strongest near poles, weaker further away |
| Long Solenoid (Inside) | Parallel straight lines | Uniform (except near ends) |
Additional Information: Magnetic Field Strength
The strength of the magnetic field (\(B\)) inside a long solenoid is given by the formula:
\( B = \mu_0 n I \)
Where:
- \(\mu_0\) is the permeability of free space (a constant, \(4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}\)).
- \(n\) is the number of turns per unit length of the solenoid (\(n = N/L\), where \(N\) is the total number of turns and \(L\) is the length).
- \(I\) is the current flowing through the solenoid.
This formula shows that the field strength inside a long solenoid depends only on the number of turns per unit length and the current, and it is uniform along the length (again, away from the ends).
Important Questions from Magnetic Field
Three infinitely long wires, each carrying equal current are placed in the xy-plane along x = 0, +d and −d. On the xy-plane, the magnetic field vanishes at
Choose the incorrect statement from the following regarding magnetic lines of field -
A wire of length L is bent in the form a circular loop. And current is passed through the loop. The magnetic field induction at the centre of the loop is B. Find the current passing through the loop.
The magnetic field at the centre of a circular coil of radius r and carrying I is B. What is the magnetic field at a distance \(x = \sqrt{3}r\) from the centre, on the axis of the coil?
Two identical coils carry equal currents and have a common center, but their planes are at right angles to each other. What is the magnitude of the resultant magnetic field at the center, if field due to one coil alone is B?
