Have you ever wondered why the magnetic field inside a solenoid does not depend on its radius whereas the magnetic field inside a circular loop or a coil depends on its radius? In this article, we will try to answer this question in simple language that even a 10th standard student can understand. So, let’s get started.
Magnetic Field and Magnetic Field Lines
Before we dive into the main question, let’s first understand what we mean by magnetic field and magnetic field lines. A magnetic field is a region in space where magnetic forces are experienced by magnetic materials. These materials could be magnets or magnetic particles like iron filings. The magnetic field is produced by moving charges like electrons or by magnetic charges or monopoles (although they are hypothetical and have not been observed yet).
The direction of the magnetic field is given by the direction of the force experienced by a north pole or a test magnetic charge placed in the field. To visualize the magnetic field, we use magnetic field lines. A magnetic field line is a curve that represents the direction of the magnetic field at every point on the curve. The direction of the magnetic field line at any point is tangent to the line at that point.
Magnetic Field of a Straight Current-Carrying Wire
Let’s start with a simple case of a straight current-carrying wire. If we pass a current through a straight wire, a magnetic field is produced around it. The magnetic field lines form concentric circles around the wire. The direction of the magnetic field is given by the right-hand rule. If we grip the wire with our right hand with our thumb pointing in the direction of the current, then the fingers give the direction of the magnetic field lines.
The magnetic field at a point depends on the distance from the wire. It decreases with distance and follows the inverse square law. If we take a point at a distance r from the wire, then the magnetic field at that point can be calculated using the formula:
B = μ0I/(2πr)
Where B is the magnetic field strength, μ0 is the permeability of free space, I is the current in the wire and r is the distance from the wire.
Magnetic Field of a Circular Loop
Now let’s move on to the case of a circular loop. If we pass a current through a circular loop, a magnetic field is produced inside and outside the loop. Inside the loop, the magnetic field lines form concentric circles around the axis of the loop. Whereas outside the loop, the magnetic field lines resemble that of a straight wire. The direction of the magnetic field inside the loop is given by the right-hand rule. If we imagine gripping the loop with our right hand such that our thumb gives the direction of the current, then the other fingers give the direction of the magnetic field lines inside the loop.
The magnetic field inside a circular loop depends on the radius of the loop. If we take only the horizontal component of the magnetic field, then it can be calculated using the formula:
Bx = μ0Ia2/(2(a2+x2)3/2)
Where Bx is the horizontal component of the magnetic field at a distance x from the center of the loop, μ0 is the permeability of free space, I is the current in the loop and a is the radius of the loop.
Magnetic Field of a Solenoid
Now comes the interesting case of a solenoid. A solenoid is a coil of many circular loops of wire, packed closely together so that they look like a single wire. If we pass a current through a solenoid, a magnetic field is produced inside the solenoid. The magnetic field lines inside the solenoid are parallel to the axis of the solenoid. The direction of the magnetic field is given by the right-hand rule. If we imagine gripping the solenoid with our right hand such that our fingers give the direction of the current, then our thumb gives the direction of the magnetic field lines inside the solenoid.
The interesting fact about the magnetic field inside a solenoid is that it does not depend on the radius of the solenoid. This means that the magnetic field inside a thin solenoid is the same as that inside a thick solenoid, as long as they have the same number of turns per unit length and carry the same current. The magnitude of the magnetic field inside a solenoid is given by the formula:
B = μ0nI
Where B is the magnetic field strength inside the solenoid, μ0 is the permeability of free space, n is the number of turns per unit length of the solenoid (also called the solenoid’s pitch) and I is the current in the solenoid.
Explanation
So, why doesn’t the magnetic field inside a solenoid depend on its radius whereas the magnetic field inside a circular loop or a coil depends on its radius?
The reason behind this lies in the way the magnetic field lines are arranged inside a solenoid. The magnetic field lines inside the solenoid are parallel to each other and in the same direction, just like the wire turns. This creates a uniform magnetic field inside the solenoid which does not depend on the radius. In contrast, in a circular loop, the magnetic field lines are more spread out and the magnetic field decreases with distance from the loop. Therefore, the magnetic field inside a circular loop or a coil depends on its radius.
Conclusion
In conclusion, we have seen that the magnetic field inside a solenoid does not depend on its radius whereas the magnetic field inside a circular loop or a coil depends on its radius. The reason behind this lies in the way the magnetic field lines are arranged inside the solenoid. The magnetic field lines inside the solenoid are parallel to each other, creating a uniform magnetic field. Whereas in a circular loop or a coil, the magnetic field lines are more spread out, creating a non-uniform magnetic field which depends on the radius.
Magnetic Field of a Solenoid Vs a Circular Loop
Have you ever wondered why the magnetic field inside a solenoid does not depend on its radius whereas the magnetic field inside a circular loop or a coil depends on its radius? In this article, we will try to answer this question in simple language that even a 10th standard student can understand. So, let’s get started.
Magnetic Field and Magnetic Field Lines
Before we dive into the main question, let’s first understand what we mean by magnetic field and magnetic field lines. A magnetic field is a region in space where magnetic forces are experienced by magnetic materials. These materials could be magnets or magnetic particles like iron filings. The magnetic field is produced by moving charges like electrons or by magnetic charges or monopoles (although they are hypothetical and have not been observed yet).
The direction of the magnetic field is given by the direction of the force experienced by a north pole or a test magnetic charge placed in the field. To visualize the magnetic field, we use magnetic field lines. A magnetic field line is a curve that represents the direction of the magnetic field at every point on the curve. The direction of the magnetic field line at any point is tangent to the line at that point.
Magnetic Field of a Straight Current-Carrying Wire
Let’s start with a simple case of a straight current-carrying wire. If we pass a current through a straight wire, a magnetic field is produced around it. The magnetic field lines form concentric circles around the wire. The direction of the magnetic field is given by the right-hand rule. If we grip the wire with our right hand with our thumb pointing in the direction of the current, then the fingers give the direction of the magnetic field lines.
The magnetic field at a point depends on the distance from the wire. It decreases with distance and follows the inverse square law. If we take a point at a distance r from the wire, then the magnetic field at that point can be calculated using the formula:
Where B is the magnetic field strength, μ0 is the permeability of free space, I is the current in the wire and r is the distance from the wire.
Magnetic Field of a Circular Loop
Now let’s move on to the case of a circular loop. If we pass a current through a circular loop, a magnetic field is produced inside and outside the loop. Inside the loop, the magnetic field lines form concentric circles around the axis of the loop. Whereas outside the loop, the magnetic field lines resemble that of a straight wire. The direction of the magnetic field inside the loop is given by the right-hand rule. If we imagine gripping the loop with our right hand such that our thumb gives the direction of the current, then the other fingers give the direction of the magnetic field lines inside the loop.
The magnetic field inside a circular loop depends on the radius of the loop. If we take only the horizontal component of the magnetic field, then it can be calculated using the formula:
Where Bx is the horizontal component of the magnetic field at a distance x from the center of the loop, μ0 is the permeability of free space, I is the current in the loop and a is the radius of the loop.
Magnetic Field of a Solenoid
Now comes the interesting case of a solenoid. A solenoid is a coil of many circular loops of wire, packed closely together so that they look like a single wire. If we pass a current through a solenoid, a magnetic field is produced inside the solenoid. The magnetic field lines inside the solenoid are parallel to the axis of the solenoid. The direction of the magnetic field is given by the right-hand rule. If we imagine gripping the solenoid with our right hand such that our fingers give the direction of the current, then our thumb gives the direction of the magnetic field lines inside the solenoid.
The interesting fact about the magnetic field inside a solenoid is that it does not depend on the radius of the solenoid. This means that the magnetic field inside a thin solenoid is the same as that inside a thick solenoid, as long as they have the same number of turns per unit length and carry the same current. The magnitude of the magnetic field inside a solenoid is given by the formula:
Where B is the magnetic field strength inside the solenoid, μ0 is the permeability of free space, n is the number of turns per unit length of the solenoid (also called the solenoid’s pitch) and I is the current in the solenoid.
Explanation
So, why doesn’t the magnetic field inside a solenoid depend on its radius whereas the magnetic field inside a circular loop or a coil depends on its radius?
The reason behind this lies in the way the magnetic field lines are arranged inside a solenoid. The magnetic field lines inside the solenoid are parallel to each other and in the same direction, just like the wire turns. This creates a uniform magnetic field inside the solenoid which does not depend on the radius. In contrast, in a circular loop, the magnetic field lines are more spread out and the magnetic field decreases with distance from the loop. Therefore, the magnetic field inside a circular loop or a coil depends on its radius.
Conclusion
In conclusion, we have seen that the magnetic field inside a solenoid does not depend on its radius whereas the magnetic field inside a circular loop or a coil depends on its radius. The reason behind this lies in the way the magnetic field lines are arranged inside the solenoid. The magnetic field lines inside the solenoid are parallel to each other, creating a uniform magnetic field. Whereas in a circular loop or a coil, the magnetic field lines are more spread out, creating a non-uniform magnetic field which depends on the radius.