Motional EMF
Motion in a magnetic field that is stationary relative to the Earth induces motional EMF (electromotive force).
Learning Objective

Identify process that induces motional electromotive force
Key Points
 Faraday's law of induction can be used to calculate the motional EMF when a change in magnetic flux is caused by a moving element in a system.
 That a moving magnetic field produces an electric field (and conversely that a moving electric field produces a magnetic field) is part of the reason electric and magnetic forces are now considered as different manifestations of the same force.
 Any change in magnetic flux induces an electromotive force (EMF) opposing that change—a process known as induction. Motion is one of the major causes of induction.
Terms

electromotive force
(EMF)—The voltage generated by a battery or by the magnetic force according to Faraday's Law. It is measured in units of volts, not newtons, and thus, is not actually a force.

magnetic flux
A measure of the strength of a magnetic field in a given area.

induction
The generation of an electric current by a varying magnetic field.
Full Text
As seen in previous Atoms, any change in magnetic flux induces an electromotive force (EMF) opposing that change—a process known as induction. Motion is one of the major causes of induction. For example, a magnet moved toward a coil induces an EMF, and a coil moved toward a magnet produces a similar EMF. In this Atom, we concentrate on motion in a magnetic field that is stationary relative to the Earth, producing what is loosely called motional EMF.
Motional EMF
Consider the situation shown in . A rod is moved at a speed v along a pair of conducting rails separated by a distance ℓ in a uniform magnetic field B. The rails are stationary relative to B, and are connected to a stationary resistor R (the resistor could be anything from a light bulb to a voltmeter). Consider the area enclosed by the moving rod, rails and resistor. B is perpendicular to this area, and the area is increasing as the rod moves. Thus the magnetic flux enclosed by the rails, rod and resistor is increasing. When flux changes, an EMF is induced according to Faraday's law of induction.
Motional EMF
(a) A motional emf=Bℓv is induced between the rails when this rod moves to the right in the uniform magnetic field. The magnetic field B is into the page, perpendicular to the moving rod and rails and, hence, to the area enclosed by them. (b) Lenz's law gives the directions of the induced field and current, and the polarity of the induced emf. Since the flux is increasing, the induced field is in the opposite direction, or out of the page. Right hand rule gives the current direction shown, and the polarity of the rod will drive such a current.
To find the magnitude of EMF induced along the moving rod, we use Faraday's law of induction without the sign:
In this equation, N=1 and the flux Φ=BAcosθ. We have θ=0º and cosθ=1, since B is perpendicular to A. Now Δ=Δ(BA)=BΔA, since B is uniform. Note that the area swept out by the rod is ΔA=ℓx. Entering these quantities into the expression for EMF yields:
To find the direction of the induced field, the direction of the current, and the polarity of the induced EMF we apply Lenz' law, as explained in Faraday's Law of Induction: Lenz' Law. As seen in Fig 1 (b), F lux is increasing, since the area enclosed is increasing. Thus the induced field must oppose the existing one and be out of the page. (The right hand rule requires that I be counterclockwise, which in turn means the top of the rod is positive, as shown. )
Electric Field vs. Magnetic Field
There are many connections between the electric force and the magnetic force. That a moving magnetic field produces an electric field (and conversely that a moving electric field produces a magnetic field) is part of the reason electric and magnetic forces are now considered as different manifestations of the same force (first noticed by Albert Einstein). This classic unification of electric and magnetic forces into what is called the electromagnetic force is the inspiration for contemporary efforts to unify other basic forces.
Key Term Reference
 Law
 Appears in these related concepts: Physics and Other Fields, Damped Harmonic Motion, and Models, Theories, and Laws
 atom
 Appears in these related concepts: Overview of Atomic Structure, Description of the Hydrogen Atom, and Stable Isotopes
 current
 Appears in these related concepts: Reporting LongTerm Liabilities, The Battery, and Magnetic Force Between Two Parallel Conductors
 electric field
 Appears in these related concepts: Maxwell's Predictions and Hertz' Confirmation, Gauss's Law, and Ampere's Law: Magnetic Field Due to a Long Straight Wire
 electromagnetic force
 Appears in these related concepts: Early Models of the Atom and Applications of Newton's Laws
 element
 Appears in these related concepts: Development of the Periodic Table, Elements and Compounds, and The Periodic Table
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 flux
 Appears in these related concepts: Applications to Economics and Biology, Surface Integrals of Vector Fields, and Faraday's Law of Induction and Lenz' Law
 force
 Appears in these related concepts: Force of Muscle Contraction, Force, and First Condition
 magnetic field
 Appears in these related concepts: Magnetic Force on a CurrentCarrying Conductor, Solenoids, Current Loops, and Electromagnets, and Brain Imaging Techniques
 magnitude
 Appears in these related concepts: Multiplying Vectors by a Scalar, Roundoff Error, and Components of a Vector
 motion
 Appears in these related concepts: Motion Diagrams, TwoComponent Forces, and Moving Source
 motional EMF
 Appears in these related concepts: A Quantitative Interpretation of Motional EMF, Electric Generators, and Mechanical Work and Electrical Energy
 perpendicular
 Appears in these related concepts: The Cross Product, Tangent Vectors and Normal Vectors, and Circular Motion
 polarity
 Appears in these related concepts: Van de Graff Generators, Water’s Polarity, and Stages of the Action Potential
 relative
 Appears in these related concepts: Relative Deprivation Approach, Addition of Velocities, and Relative Velocity
 resistor
 Appears in these related concepts: Impedance, The Loop Rule, and Introduction and Importance
 right hand rule
 Appears in these related concepts: Angular Quantities as Vectors, Gyroscopes, and Direction of the Magnetic Force: The Right Hand Rule
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