Right Hand Rule in Physics
The right hand rule is a hand mnemonic used in physics to identify the direction of axes or parameters that point in three dimensions.Invented in the 19th century by British physicist John Ambrose Fleming for applications in electromagnetism, the right hand rule is mostoften used to determine the direction of a third parameter when the other two are known (magnetic field, current, magnetic force).There are a few variations of the right hand rule, which are explained in this section.
When a conductor, such as a copper wire, moves through a magnetic field (B), an electric current (I) is induced in the conductor.This phenomenon is known as Faraday's Law of Induction. If the conductor is moved inside the magnetic field, then there is a relationshipbetween the directions of the conductor's motion (velocity), magnetic field and the induced current. We can use Fleming's right hand ruleto investigate Faraday's Law of Induction, which is represented by the equation:
emf = induced emf (V or J/C)
N = number of turns of coil
Δ𝚽B = change in the magnetic flux (Tm2)
Δt = change in time (s)
Because the x, y and z axes are perpendicular to one another and form right angles, the right hand rule can be used to visualize theiralignment in three-dimensional space. To use the right hand rule, begin by making an L-shape using your right thumb, pointer and middlefinger. Then, move your middle finger inwards toward your palm, so that it is perpendicular to your pointer finger and thumb. Your handshould look similar to this:
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.
Teaching Tools
Wireless Smart Cart
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.
Many teachers use a rotating meterstick to show that an object, which appears to be rotating “clockwise” from one student’s perspective, also appears to be rotating “counter-clockwise” when viewed from an alternative perspective.Using a dynamics cart to teach the right hand rule enables educators to demonstrate both the problem with “clockwise” and “counter-clockwise” terminology, as well as the solution that the right hand rule and rotational axes provide.With the Wireless Smart Cart, educators can leverage the 3-axis gyroscope and fixed coordinate system to create engaging demonstrations in rotational motion.Check out the full demonstration here.
Right Hand Rule for Magnetism
Moving Charges
A charged particle is a particle with an electric charge. When a motionless charged particle exists in a magnetic field, it does notexperience a magnetic force; however, as soon as the charged particle moves within a magnetic field, it experiences an induced magneticforce that displaces the particle from its original path. This phenomenon, also known as Lorentz force, is consistent with the rule thatstates, "magnetic fields do no work.” The equation used to determine the magnitude of the magnetic force acting on a charged particle (q)moving a magnetic field (B) with a velocity of v at an angle of θ is:
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.
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.
The right hand rule states that: to determine the direction of the magnetic force on a positive moving charge, point your right thumb inthe direction of the velocity (v), your index finger in the direction of the magnetic field (B), and your middle finger will point in thedirection of the the resulting magnetic force (F). Negative charges will be affected by a force in the opposite direction.
Current-Induced Magnetic Force: Current in a Straight Wire
A conventional current is composed of moving charges that are positive in nature. When a conventional current moves through a conducting wire,the wire is affected by a magnetic field that pushes it. We can use the right hand rule to identify the direction of the force acting on thecurrent-carrying wire. In this model, your fingers point in the direction of the magnetic field, your thumb points in the direction of theconventional current running through the wire, and your palm indicates the direction that the wire is being pushed (force).
The magnetic force acting on a current-carrying wire is given by the equation:
When the length of the wire and the magnetic field are at right angles to one another, then the equation becomes:
FB = magnetic force (N)
I = current (A)
L = length of wire (m)
B = magnetic field (T)
If we consider current flow as the movement of positive charge carriers (conventional current) in the aboveimage, we notice that the conventional current is moving up the page. Since a conventional current is composedof positive charges, then the same current-carrying wire can also be described as having a current with negativecharge carriers moving down the page. Although these currents are moving in opposite directions, a singlemagnetic force is observed acting on the wire. Therefore, the force occurs in the same direction whether weconsider the flow of positive or negative charge carriers in the above image. Applying the right hand rule tothe direction of the conventional current indicates the direction of the magnetic force to be pointed right.When we consider the flow of negative charge carriers in the above image, the right hand rule indicates thedirection of the force to be left; however, the negative sign reverses the result, indicating that the directionof the magnetic force is indeed pointing right.
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. As a result, the right hand rule indicates that the magneticforce is pointing in the left direction.
Currents Induced by Magnetic Fields
While a magnetic field can be induced by a current, a current can also be induced by a magnetic field. We can usethe second right hand rule, sometimes called the right hand grip rule, to determine the direction of the magneticfield created by a current. To use the right hand grip rule, point your right thumb in the direction of the current'sflow and curl your fingers. The direction of your fingers will mirror the curled direction of the induced magnetic field.
The right hand grip rule is especially useful for solving problems that consider a current-carrying wire or solenoid.In both situations, the right hand grip rule is applied to two applications of Ampere's circuital law, which relatesthe integrated magnetic field around a closed loop to the electric current passing through the plane of the closed loop.
Rotational Direction: Solenoids
When an electric current passes through a solenoid, it creates a magnetic field. 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. They wrap around from the inside tothe outside of the solenoid.
Rotational Direction: Current-Carrying Wires
When an electric current passes through a straight wire, it induces a magnetic field. To apply the right hand grip rule,align your thumb with the direction of the conventional current (positive to negative) and your fingers will indicate thedirection of the magnetic lines of flux.
Right Hand Rule for Torque
Torque problems are often the most challenging topic for first year physics students. Luckily, there's a right hand ruleapplication for torque as well. 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.
The equation for calculating the magnitude of a torque vector for a torque produced by a given force is:
When the angle between the force vector and the moment arm is a right angle, the sine term becomes 1 and the equationbecomes:
F = force (N)
𝜏 = torque (Nm)
r = distance from center to line of action (m)
Positive and Negative Torques
Torques that occur in a counter clockwise direction are positive torques. Alternatively, torques that occur in theclockwise direction are negative torques. So what happens if your hand points in or out of the paper? Torques thatface out from the paper should be analyzed as positive torques, while torques that face inwards should be analyzedas negative torques.
Right Hand Rule for a Cross Product
A cross product, or vector product, is created when an ordered operation is performed on two vectors, a and b. Thecross product of vectors a and b, is perpendicular to both a and b and is normal to the plane that contains it. Sincethere are two possible directions for a cross product, the right hand rule should be used to determine the directionof the cross product vector.
For example, the cross product of vectors a and b can be represented using the equation:
(pronounced “a cross b”)
To apply the right hand rule to cross products, align your fingers and thumb at right angles. Then, point your indexfinger in the direction of vector a and your middle finger in the direction of vector b. Your right thumb will pointin the direction of the vector product, a x b (vector c).
Right Hand Rule for Lenz's Law
Lenz's law of electromagnetic induction is another topic that often seems counterintuitive, because it requiresunderstanding how magnetism and electric fields interact in various situations. Lenz's law states that the directionof the current induced in a closed conducting loop by a changing magnetic field (Faraday's Law) is such that thesecondary magnetic field created by the induced current opposes the initial change in the magnetic field that producedit. So what does this mean? Let's break it down.
When the magnetic flux through a closed loop conductor changes, it induces a current within the loop. 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.
𝚽B = magnetic flux (Tm2)
B = magnetic field (T)
Θ = angle between field and normal (deg)
A = area of loop (m2)
To understand how Lenz's Law will affect this system, we need to first determine whether the initial magnetic field isincreasing or decreasing in strength. As the magnetic north pole gets closer to the loop, it causes the existing magneticfield to increase. Since the magnetic field is increasing, the induced current and resulting induced magnetic field willoppose the original magnetic field by reducing it. This means that the primary and secondary magnetic fields will occur inopposite directions. 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.
To apply the right hand rule to Lenz's Law, first determine whether the magnetic field through the loop is increasing ordecreasing. Recall that magnets produce magnetic field lines that move out from the magnetic north pole and in toward themagnetic south pole. If the magnetic field is increasing, then the direction of the induced magnetic field vector will bein the opposite direction. If the magnetic field in the loop is decreasing, then the induced magnetic field vector willoccur in the same direction to replace the original field's decrease. Next, align your thumb in the direction of theinduced magnetic field and curl your fingers. Your fingers will point in the direction of the induced current.
