Torque experienced by a current loop in a uniform magnetic field

A Current Loop in a Uniform Magnetic Field Experiences Torque

In a homogeneous magnetic field B, we examine a rectangular current loop PQRS with sides a and b preserved vertically. Let be the angle formed by B’s direction and the vector perpendicular to the loop’s plane. Taking into account the two straight portions PQ and RS. These pieces are subjected to forces that are clearly equal in magnitude and opposite in direction. Because the forces acting on each other are collinear, the net force attributable to this pair is zero. The torque produced by this set of forces has a lever arm of bsin. F1 = BIa is the magnitude of each force. Similarly, we can write F2 = IBb = F1 as the expression for a force F2 exerted on the arm RS.

The loop’s torque is given by:

τ = F1a/2 + F2 a/2

τ = IbB a/2 + IbB a/2 = I(ab) B = IAB

The coil’s area is denoted by the letter A. The loop revolves in a counterclockwise direction due to torque.

Torque Experienced by a Current Loop, in a Magnetic Field

Consider the situation where the plane of the loop is not parallel to the magnetic field. Let’s call the angle created by the field and the coil’s normal. The forces acting on the arms QR and SP will always be equal in size and will always act in opposite directions, as can be seen. The results of these forces cancel out because they are equal opposites and collinear at all points, resulting in zero-force or torque. The forces on the arms PQ and RS are determined by F1 and F2. These forces are similar in size and direction and can be produced by,

F1 = F2 = IbB

Because the forces are not collinear, they work as a couple, causing torque to be applied to the coil. The torque’s magnitude can be expressed as:

τ = F1a/2 sinθ + F2 a/2 sinθ

τ = IabBsinθ

τ = IABsinθ

The explanation for Torque on Current Loop

When you apply pressure to an object, it moves or exerts a certain amount of force. For example, spinning the cap off a bottle, removing the lid from a package, opening the doorknob, tying a shoelace, and so on. These are rotational motions, which are movements with some movement involved. Torque is a phrase that refers to the spinning movement that all items have and that we would be unable to operate properly without. The formula for torque is τ = Fr. because torque is equivalent to the twisting force that tends to generate movement or rotation. This formula is used when force (f) is applied to an item depending on the distance (r) between the centre of rotation and the location where the force is applied. To establish the direction of the torque, apply the right-hand rule: right-hand fingers should point in the direction of the current, and the thumb should stick out and point to the area vector.

Torque on Current Loop – The Magnetic Moment

The magnetic moment of a current loop can be calculated using the product of the current flowing in the loop and the area of the rectangular loop. m = IA is a mathematical formula.

The area of the rectangular loop determines the magnitude of A, while the direction is determined by the right-hand thumb rule. As indicated in the previous equation, the torque exerted on a current-carrying coil placed in a magnetic field can be determined using the vector product of the magnetic moment and the magnetic field.

τ = m×B

Applications of Torque

• Moving Coil Galvanometer: It is used to measure current in a circuit by using a moving coil galvanometer. It works on the premise of a torque being experienced by a current-carrying coil in a uniform magnetic field. It’s constructed out of a rectangular coil twisted with a large number of turns of thin insulated copper wire around a light metallic frame. The coil is suspended between the pole components of a horse-shoe magnet by a fine phosphor – bronze strip from a movable torsion head. Only a few twists connect the coil’s bottom end to a phosphor bronze hairspring (HS). The binding screw is joined to the other end of the spring. Inside the coil is a symmetrical soft iron cylinder. The hemispherical magnetic poles produce electricity in all of their positions. The hemispherical magnetic poles form a radial magnetic field in which the coil’s plane is parallel to the magnetic field in all of its positions. A small plane mirror (m) attached to the suspension wire, along with a lamp and scale arrangement, is used to measure the coil’s deflection.

• Conversion of Galvanometer into an Ammeter: A galvanometer is an electrical instrument that measures current flow in a circuit. Despite the fact that the deflection is proportional to the current, the galvanometer scale is not labelled in ampere. A large current cannot be passed through the galvanometer without breaking the coil because it is such a fragile device. A galvanometer, on the other hand, can be converted to an ammeter by putting it in parallel to low resistance. As a result, when a large amount of current flows through a circuit, only a small percentage of it travels through the galvanometer, with the rest passing via the low resistance. The low resistance connected in parallel with the galvanometer is known as shunt resistance. Amperes are measured on the scale.

• Pointer type moving coil Galvanometer: Galvanometers with suspended coils have a high sensitivity. They have the ability to measure currents on the order of 10⁻⁸ amperes. As a result, galvanometers must be treated with caution. When sensitivity isn’t necessary, pointer type galvanometers are used in the lab for experiments like Wheatstone’s bridge. In this type of galvanometer, the coil pivots on ball bearings. A lighter aluminium pointer attached to the coil slides across a scale as the current is passed. The restorative couple is provided by a spring.

• Conversion of Galvanometer into Voltmeter: A voltmeter is a device that determines the potential difference between two current-carrying conductor ends. It can be converted into a voltmeter by connecting a high resistance to a galvanometer. To calibrate the scale, use the volt scale.

• Voltage Sensitivity of a Galvanometer: A galvanometer’s voltage sensitivity is defined as the deflection per unit voltage.

∴ Voltage sensitivity θ/v = θ/IG =nBA/CG

The galvanometer resistance is denoted by G.

• Galvanometer Current Sensitivity: A galvanometer’s current sensitivity is defined as the deflection that occurs when unit current travels through it. When a galvanometer produces a considerable deflection for a tiny current, it is said to be sensitive.

I = C/nBAθ in a galvanometer

As a result, Current Sensitivity θ/I = nBA/C

CONCLUSION

We saw in this article that under a homogeneous magnetic field, the torque on a current-carrying loop of any shape equals

τ = NIABsinθ

N is the number of turns, I is current, A is the loop’s area, B is the magnetic field’s strength, and is the angle between the loop’s perpendicular and the magnetic field.