The direction of your fingers will mirror the curled direction of the induced magnetic field. If we consider the flow of charges in two different wires, one with positive charges flowing up the page, and onewith negative charges flowing up the page, then the direction of the magnetic forces will not be the same, becausewe are considering two different physical situations. In the first wire, the flow of positive charges up the pageindicates that negative charges are flowing down the page. Using the right hand rule tells us that the magneticforce will point in the right direction. In the second wire, the negative charges are flowing up the page, whichmeans the positive charges are flowing down the page.

The right-hand rule dates back to the 19th century when it was implemented as a way for identifying the positive direction of coordinate axes in three dimensions. William Rowan Hamilton, recognized for his development of quaternions, a mathematical system for representing three-dimensional rotations, is often attributed with the introduction of this convention. In the context of quaternions, the Hamiltonian product of two vector quaternions yields a quaternion comprising both scalar and vector components.[1] Josiah Willard Gibbs recognized that treating these components separately, as dot and cross product, simplifies vector formalism. Following a substantial debate,[2] the mainstream shifted from Hamilton’s quaternionic system to Gibbs’ three-vectors system. This transition led to the prevalent adoption of the right-hand rule in the contemporary contexts. You can do this in reverse by starting your thumb in the direction of the vector and see how your fingers curl to see the direction of rotation.

## Fleming’s Left-Hand Rule and Fleming’s Right-Hand Rule

It is often useful to be able to remember which way the field points (the direction a compass needle will point) when placed near the wire. Unlike most mathematical concepts, the meaning of a right-handed coordinate system cannot be expressed in terms of any mathematical axioms. Rather, the definition depends on chiral phenomena in the physical world, for example the culturally transmitted meaning of right and left hands, a majority human population with dominant right hand, or certain phenomena involving the weak force. Find the direction of the magnetic field if an electron is moving vertically upwards and gets deflected towards the south due to a uniform magnetic field.

## Current-Induced Magnetic Force: Current in a Straight Wire

When the electron moves upward, the direction of the current is in the opposite direction; that is, the direction of the current is downwards. It is given that the proton is moving towards the east, and therefore, the motion of the current is towards the east. The direction of force is towards the north as the magnetic field is acting downwards.

Fleming’s right-hand rule is used to determine the direction of the induced current. To use the right hand grip rule ina solenoid problem, point your fingers in the direction of the conventional current and wrap your fingers as if theywere around the solenoid. Your thumb will point in the direction of the magnetic field lines inside the solenoid. Notethat the magnetic field lines are in the opposite direction outside the solenoid. A cross product, or vector product, is created when an ordered operation is performed on two vectors, a and b.

## Rotational Direction: Solenoids

Determine the direction of the force acting on the proton if the proton moves towards the east by entering a uniform magnetic field in the downward direction. One of the best ways to help students become confident using the right hand rule, is to perform a visual demonstration that helps them recognize and correct their misconceptions about orthogonal relationships and coordinate systems. In the diagram above, the thumb aligns with the z axis, the index finger aligns with the x axis and the middle finger aligns with the y axis.

The inducedcurrent creates a secondary magnetic field that opposes the original change in flux that initiated the induced current.The strength of the magnetic field passing through a wire coil determines the magnetic flux. Magnetic flux depends onthe strength of the field, the area of the coil, and the relative orientation between the field and the coil, as shownin the following equation. The plane formed by the direction of the magnetic field and the charged particle’s velocity is at a right angle to the force. Because theforce occurs at a right angle to the plane formed by the particle’s velocity and the magnetic field, we can use the right hand rule todetermine their orientation. When a current-carrying conductor is placed in an external magnetic field, the conductor experiences a force perpendicular to both the field and the current flow’s direction.

When the existing magnetic field is decreasing, the induced current and resulting induced magneticfield will oppose the original, decreasing magnetic field by reinforcing it. Thus, the induced magnetic field will have thesame direction as the original magnetic field. When the magnetic flux through a closed loop conductor changes, it induces a current within the loop.

- Ampère was inspired by fellow physicist Hans Christian Ørsted, who observed that needles swirled when in the proximity of an electric current-carrying wire and concluded that electricity could create magnetic fields.
- Although these currents are moving in opposite directions, a singlemagnetic force is observed acting on the wire.
- It is important to note that these rules do not determine the magnitude; instead show only the direction of the three parameters (magnetic field, current, force) when the direction of the other two parameters is known.
- For left-handed coordinates, the above description of the axes is the same, except using the left hand; and the ¼ turn is clockwise.
- Your thumb will point in the direction of the magnetic field lines inside the solenoid.
- The inducedcurrent creates a secondary magnetic field that opposes the original change in flux that initiated the induced current.The strength of the magnetic field passing through a wire coil determines the magnetic flux.

## Coordinates

Consequently, we can say that the direction of the force acting is towards the north. Using Fleming’s left-hand right hand grip rule rule, we can determine the direction of force acting on the proton. When a charged particle, such as a proton or electron, moves it causes a magnetic effect. It is, in fact, the movement of the electrons in the molten iron core that create the Earth’s magnetic fieldclosemagnetic fieldArea surrounding a magnet that can exert a force on magnetic materials.. In vector calculus, it is necessary to relate a normal vector of a surface to the boundary curve of the surface.

Given a surface S with a specified normal direction n̂ (a choice of “upward direction” with respect to S), the boundary curve C around S is defined to be positively oriented provided that the right thumb points in the direction of n̂ and the fingers curl along the orientation of the bounding curve C. In this episode of Class 10 One-Shot Series, we take up CBSE Class 10 Science Chapter 13 – Magnetic Effects of Electric Current. We help you understand all concepts related to the Magnetic Field, Magnetic Field Due to a Current-Carrying Conductor, Oersted’s experiment, Right-hand thumb rule, Fleming’s left-hand rule, Faraday’s experiment, Fleming’s right-hand rule, and Electromagnetic induction. The fields can be investigated by looking at the effects of the forces they exert on other magnets and magnetic materials. For left-handed coordinates, the above description of the axes is the same, except using the left hand; and the ¼ turn is clockwise. Torques thatface out from the paper should be analyzed as positive torques, while torques that face inwards should be analyzedas negative torques.

To use the right hand rule in torque problems, take your right hand and point it in thedirection of the position vector (r or d), then turn your fingers in the direction of the force and your thumb will pointtoward the direction of the torque. If you have two vectors that you want to cross multiply, you can figure out the direction of the vector that comes out by pointing your thumb in the direction of the first vector and your pointer in the direction of the second vector. If the velocity of the charged particle is parallel to the magnetic field (or antiparallel), then there is no force because sin(θ) equals zero.When this occurs, the charged particle can maintain its straight line motion, even in the presence of a strong magnetic field.

What gives the magnitude of force along this direction determined by these rules is the Lorentz’ Force. For right-handed coordinates, if the thumb of a person’s right hand points along the z-axis in the positive direction (third coordinate vector), then the fingers curl from the positive x-axis (first coordinate vector) toward the positive y-axis (second coordinate vector). When viewed at a position along the positive z-axis, the ¼ turn from the positive x- to the positive y-axis is counter-clockwise. Using Fleming’s left-hand rule, we can determine the direction of the magnetic field acting on the electron. Fleming’s Left-Hand Rule and Fleming’s Right-Hand Rule are essential rules applicable in magnetism and electromagnetism. John Ambrose Fleming developed them in the late 19th century as a simple way of working out the direction of electric current in an electric generator or the direction of motion in an electric motor.