# Magnetic Field At The center Of Loop (9 Interesting Facts)

A magnetic field is a vector field that illuminates the magnetic bump on the motion of electrostatic charge, electric power, and magnetic materials. A movement of charges in a magnetic field comprises a force vertical to its velocity and the magnetic field.

The magnetic field at the center of the Loop is. B = 2πμ0I = 2πAμ0I or I =μ02BπA. The magnetic moment of the Loop is. M = IA =2BA . The magnetic field at the center of the Loop is zero because, at a point adjacent to the center exterior of the solenoid, the magnetic fields due to nearest loops are identical in the immensity and reverse in supervision.

## The magnetic field of a loop current

Studying the orientation of the magnetic field generated by a current conveying section of wire indicates that entire parts of the Loop share a magnetic field in a similar orientation inwards the Loop. The electric current in a circular loop produces a more highly consolidated magnetic field in the centre of the Loop than in the outside Loop. They are mounding numerous loops that compact the field even higher into what is called a solenoid.

Let us determine the magnetic field in a circular loop; when we proceed with the electric current along the Loop, a magnetic field has generated the orientation of the magnetic field is given by the Right-hand thumb rule. Applying the Right-hand thumb rule, we obtain a magnetic field in the form of concentric circles adjacent to the current conveying wire.

As we draw away from wires, the circles become larger and larger. When we attain the Loop’s center, the trajectory arrives as a linear line. Magnetic field due to loop current relies on the immensity of electrical current – higher current, higher magnetic field diameter of circular Loop – higher diameter, smaller the electric field.

## Direction of magnetic field between two parallel lines

The direction of the magnetic field in two parallel lines between two parallel lines can be detected by utilizing Ampere’s right-hand grip rule. If we emplacement our right-hand thumb in the direction of current in the wire, bowed fingers point out the direction of the magnetic field lines. Observe that two wires conveying current in a similar direction captivate one another and revolt if the currents are reversed.

To find out the net magnetic field in the middle between the two wires, we must determine the magnetic field as a consequence of every wire and then pick up the summation of those two vectors. Hence the electric current moves in the reverse direction in two wires. We must minus the two vectors to find out the total magnetic field.

Once the magnetic field has been deliberated using B=μ0I/2πr, the magnetic force expression can be utilized to deliberate the force. The direction is acquired from the right-hand rule. At one point we have premeditated the force one second wire, the force on the wire must be equal in the immensity and the inverse orientation.

## What is the magnetic field at the centre of the Loop?

The magnetic field at the centre of the Loop is. B = 2πμ0I = 2πAμ0I or I =μ02BπA. The magnetic moment of the Loop is. M = IA =2BA . The magnetic field at the centre of the Loop is zero because, at a point nearby the centre outermost of the solenoid, the magnetic fields because of the nearest loops are similar in the immensity and reverse in orientation.

The electric current in a circular loop produces a magnetic field more absorbed in the Loop’s centre than in the exterior Loop. And the situation of various loops is called a solenoid, and its centre is called the centre of the solenoid. At the centre, the entire segments of the Loop are at an identical separation. So, the field lines become straight, and the magnetic field at the Loop’s centre will be zero.

Let us draw the circle considering the upper part of the circle P and the lower part of the circle Q. Let us suppose that A and B are the sides of the circle and C is the circle’s center. The magnetic field due to the upper partway is equal and opposite to the lower partway. So, the magnetic field at the center of the Loop is zero.

## How to calculate the magnetic field at the center

The magnetic field at the centre of the circular loop in the circuit conveying current I shown in following figure. By using this figure we can calculate the magnetic field at the center of loop.

Magnetic field due to circular loop is given by,

B1 = μ0I/2r

B1 = ( μ0I/4πr)×2π

Magnetic field due to straight wire is given by,

B2 = μ0I/2r

B2 = ( μ0I/4πr)×2

Therefore, net magnetic field is given by subtracting two magnetic field

B1-B2 = ( μ0I/4πr) (2π-2)

The magnetic field at the centre of the loop is given by the equation,

= (μ0/4π) × (2I/r) (π-1)

The simplified form to calculate magnetic field at the centre of the loop is given by

B0 = μ0I/2R

Now, to find magnetic field at the centre of an arc subtending the angle Ɵ at the centre (B)

Since for circle (Ɵ=2π) == μ0I/2R

For arc (Ɵ) = B

Cross multiplying the above equation then we get the magnetic field

B = μ0IƟ/4πR

This equation is used to calculate the magnetic field at the centre of the loop.

## Why is the magnetic field maximum at the centre?

The durability of the magnetic field is conversely comparable to its source point. The more durable the magnetic field, the closer it is to the source. Origin will be the centre of the Loop. There is just one point desirable closest to the Loop: the origin. The magnetic field is at the centre of a current carrying loop.

The magnetic field is maximum at the Loop’s centre because such magnetic force lines enclose every tiny section of the coil. At the centre of the current carrying coil, entire lines of force hold up each other, as a consequence of which the durability of the magnetic field increases.

The direction of the magnetic field is at the inclination to the coil’s seat at the Loop’s centre. Hence, the magnetic fields arrive as coaxial circles, and at the centre, the diameter is greater than other points. The magnetic fields are greater or maximum at the centre.

## What is the value of the magnetic field at the centre of a square loop?

The value of the magnetic field at the centre of a square loop is equal to B=2πaμI. Suppose if the magnetic field due to a square loop of side a carrying current I at its centre is equal to √2μ0I/πa.

Suppose MNOP is a square loop consisting of constant conducting wire. Suppose the current arrives at the Loop at M and departs at P. In that case, the magnetic field will be maximum at the centre of the Loop because the magnetic field is inversely proportional to the distance of separation that B=μI/2πd gives.

Suppose the square loop ABCD with edge length a. The opposition of the wire ABC is r, and that of ADC is 2r. The magnetic field’s value at the square Loop’s centre, assuming a uniform wire, is √2μ0I/3πa.

## Can the magnitude of the magnetic field at the centre be zero?

Yes, the magnitude of the magnetic field at the centre is zero. It happens because the field lines nearer to the centre are auxiliary to the length of the diamagnetic. As well as, the stability of the field line is larger at the poles of the diamagnetic and smaller at the centre. This means that the magnitude of the magnetic field at the centre is zero.

The magnetic field at O due to MN will be similar to that due to PQ but in reverse orientation, so the magnitude of the magnetic field at the centre would be zero. For example, if a bar magnet is kept in a constant magnetic field B, its poles +m and –m expertise force MB and MB through reverse supervision of the magnetic field, so the magnitude of the magnetic field at the centre is zero.

Consider the centre of the bar magnet. If we consider a plane moving along the centre, there will be an equal number of dipoles on every side, with negative polarities. As such, the magnetic field falls out and dribbles zero magnitudes of the magnetic field at the centre.

## Practice problem

A circular coil of radius π cm and 100 turns carries a current of 10A. Find the magnitude of the magnetic induction field at the centre of the coil?

Solution:

Given the data: the radius is r = π cm

The current I= 10A

Number of turns of the coil n = 100 cm

We have to find the magnetic field of the magnetic induction field at the centre of the coil.

B = KI/r

Where K =μ0/2

B = μ0I/2r this is the formula to find out the magnetic field strength.

So,  μ0 =4π×10-7

Substitute the value of μ0 , I and r in the equation of magnetic field strength

B = μ0I/2r

B=4π×10-7×10×100/2×(π)

B = 2×10-4 Tesla

1. Calculate the magnetic field at the centre of a square loop which carries a current of 1.5A, length of each loop is 50 cm.

Current carries along a square loop

I = 1.5 A

Length of each loop, l =50 cm = 50×10-2 m

Magnetic field at the centre of the square loop B =?

Magnetic field due to current carrying straight conductor according to Biot-savart law is given by

B = (μ0I/4πa)[sin ø1 + sin ø2]

a=1/2, ø1=450, ø2=450

For a square it has 4 sides. So  at the centre of a square, the magnetic field

B = 4 × (μ0I/4πl/2)[sin ø1 + sin ø2]

= (4 × 4π × 10-7 × 1.5/ 4π × 50 × 10-2/2)[1/√2 + 1/√2 ]

=( 4 × 1.5 × 2 × 10-7/√2  × 25 × 10-2)

= (12 × 10-7/1.414 × 25 × 10-2)

= .3395 × 10-5

B = 3.4 × 10-6  T

## Why are magnetic fields straight in the centre of current carrying circular loops?

Magnetic field lines are sealed circular loops. Circular loops are mostly long straight wire twisted in the form of a circle because the field lines about a current carrying wire are coaxial circles or concentric circles. (for better understanding, see the images for magnetic field lines about a straight wire and a current carrying loop).

At the circle’s centre, each field line is at constant separation. Thus they employed uniform compulsion on one another and bowed into a similar orientation. Although any other point inwards, the circle should be nearer to one point than another.

Consequently, the Loop fragment nearer to the inspection point shall have a magnetic field line that applies much more compulsion and twists it in its orientation. Hence the inspection point reclines nearer, and the magnetic field increases with the decrease of separation. But at the centre, every part of the Loop is at a constant distance. Hence the field lines become straight.

## Do magnetic fields move?

Yes, the magnetic fields can move. They move with the captivated gadget as in a generator. The varying magnetic field produces electricity. The sun creates a strong magnetic field, but it is also revolving. These fields did not revolve at the same rate as the sun and bear to get preferably deviant up.

The plasma or warm gases confined in those fields can get strained off when those knotted fields have sufficient energy or withstand the sun gyration ample supply.This is called a solar flare with a solar mass emission.

Solar flares bring imposed particles like helium nuclei called alpha particles. They can hurt the satellite and communications momentarily or enduringly when stronger enough. Auspiciously, these particles’ sleets move much more deliberately than the light from the sun, and we can notice them in time to close below key systems on the satellite to save them.

## What is magnetic field intensity?

The magnetic field intensity is defined as “a proportion of the magneto-motive force required to generate a definite flux density enclosed by a specific material per unit length of that material. We can also say that magnetic field intensity is magnetic field strength potency proceeding on a unit magnetic pole”.

The segment of the magnetic field in a substance that appears from an outward current is not inherent to the substance itself. Magnetic field intensity is also called magnetic field strength, represented by the symbol H, and it has both magnitude and direction; hence it is a vector quantity.

The degree to which a magnetic field can influence a material or the potentiality of the outermost magnetic field to fascinate the material is known as magnetic intensity. The magnetic field generated by the outward origin of current is called magnetizing.

#### Conclusion

The magnetic field at the centre of a circular loop is an exceptional case of a magnetic field through the axis of a circular loop. The magnetic field in the wire can vary by curving the wire into a circular loop. The magnetic field can be determined using Biot-Savart law and Ampere Circuit law.

Megha BR

Hi, I am Megha B R, I have completed my Post-Graduation in Solid State Physics and pursuing B. Ed. I am a Physics enthusiast. As an Academic writer, my goal is to reach the readers in a simplified manner through my articles. Let's connect through LinkedIn-https://www.linkedin.com/in/megha-br-08a129206