Why is an emf induced in a straight rod moved at right angles across a magnetic field?

The free electrons in the rod travel with it through the field, so each feels a force Bqv directed along the rod. They gather at one end and leave the other end positive, so a potential difference appears between the ends.

Derive the expression for the emf induced in a rod of length l moving with speed v at right angles to a field of flux density B.

In a time t the rod sweeps out an area lvt, so the flux it cuts is Blvt. Dividing that change of flux by the time t gives an emf of Blv.

Which end of a moving rod becomes positive?

The end towards which conventional current would be driven becomes positive. Fleming's right-hand rule finds it, with the first finger along the field and the thumb along the motion.

A rod 0.80 m long moves at 12 m s⁻¹ at right angles to a field of 0.050 T. Calculate the emf induced across it.

The emf is E = Blv = 0.050 × 0.80 × 12 = 0.48 V. Dividing 0.48 V by 0.050 T and by 0.80 m returns a speed of 12 m s⁻¹.

Eduqas A-Level Physics A420QS

Basic Physics

Topic overview SI base units and prefixes Checking equations for homogeneity Scalars and vectors Adding and resolving vectors Density Moments and the principle of moments Centre of gravity and equilibrium

Kinematics

Topic overview Displacement, velocity and acceleration Displacement-time graphs Velocity-time graphs and non-uniform acceleration The equations of uniformly accelerated motion Free fall, air resistance and terminal velocity Projectile motion

Dynamics

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Circular Motion

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Kinetic Theory

Topic overview The ideal gas equation of state Assumptions of the kinetic theory of gases The Avogadro constant, the mole and molar mass The kinetic theory pressure equation Molecular kinetic energy and temperature

Thermal Physics

Topic overview Internal energy Absolute zero and temperature Internal energy of an ideal monatomic gas Heat as energy in transit Thermal equilibrium Work done by a gas The first law of thermodynamics Specific heat capacity

Conduction of Electricity

Topic overview Electric charge and the coulomb Electric current and the ampere Conductors, insulators and charge carriers Drift of free electrons in a metal Deriving and using I = nAve

Resistance

Topic overview Potential difference and the volt Resistance, Ohm's law and the ohm I–V characteristics of a metal wire and a filament lamp Electrical power and energy transfer The microscopic origin of resistance Resistivity and the equation R = ρl/A Resistance and temperature Superconductivity and the transition temperature High temperature superconductors and their uses

D.C. Circuits

Topic overview Current at a junction and conservation of charge Potential difference round a circuit and conservation of energy Resistors in series Resistors in parallel The potential divider Sensing circuits with LDRs and thermistors emf and internal resistance

Capacitance

Topic overview The parallel plate capacitor and stored charge Capacitance and the farad The capacitance of a parallel plate capacitor Dielectrics The uniform field between the plates and E = V/d Energy stored in a capacitor Capacitors in series and in parallel Charging and discharging through a resistor

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Wave Properties

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Photons

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Lasers

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Nuclear Decay

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Particles and Nuclear Structure

Topic overview The Rutherford alpha particle scattering experiment Coulomb repulsion in the plum pudding and Rutherford models Quarks and leptons: the first generation Antiparticles, annihilation and their symbols Hadrons: baryons, antibaryons and mesons Quark composition of the proton, neutron and pions The four fundamental interactions Conservation laws in particle reactions

Nuclear Energy

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Magnetic Fields

Topic overview The motor effect and Fleming's left-hand rule F = BIl sinθ and measuring magnetic flux density The force on a moving charge, F = Bqv sinθ The Hall effect and the Hall probe Magnetic fields due to a straight wire and a solenoid Forces between current-carrying conductors Charged particle beams and accelerators

Electromagnetic Induction

Topic overview Magnetic flux, flux linkage and the weber Faraday's law and Lenz's law Applying the laws: emf from rate of change of flux linkage Emf induced in a linear conductor moving through a field The rotating coil and the a.c. generator

Option A: Alternating CurrentsOption A

Topic overview Electromagnetic induction in a rotating coil Frequency, period, peak and rms values Mean power dissipated in a resistor Using an oscilloscope to measure voltage and frequency Inductors in a.c. circuits and inductive reactance Capacitors in a.c. circuits and capacitive reactance Phasors, phase angle and impedance Resonance in the series RCL circuit and the Q factor

Option B: Medical PhysicsOption B

Topic overview The nature and properties of X-rays X-ray production and controlling the beam Attenuation of X-rays and half-value thickness X-ray imaging, fluoroscopy and radiography Computed tomography scanning Ultrasound generation and acoustic impedance Ultrasound scanning and the Doppler technique Magnetic resonance and MRI Radiation effects on living matter and dosimetry Radionuclide tracers, the gamma camera and PET

Option C: The Physics of SportsOption C

Topic overview Centre of gravity, stability and toppling Moments in muscle systems and other sporting contexts Impulse and Newton's second law in sport The coefficient of restitution Moment of inertia Angular acceleration, torque and angular momentum Conservation of angular momentum and rotational energy Projectiles, Bernoulli's equation and drag

Option D: Energy and the EnvironmentOption D

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Mathematical Requirements (Appendix C)

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How Science Works

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Electromagnetic Induction

Emf induced in a linear conductor moving through a field

3 things to know
Component 3

Overview

Recall questions on E = Blv with every symbol, its derivation from the rate at which flux is cut, why the conductor must cut the field lines, Fleming's right-hand rule for the direction, and worked calculations for a rod moving on rails.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

State the expression for the emf induced in a moving linear conductor, defining every symbol and its unit.

Key term

State Fleming's right-hand rule and say when it is used.

Key term

Why does only the vertical component of the Earth's field matter for an aircraft flying level?

Questions from this subtopic

Each one with the model answer underneath.

1
Why is an emf induced in a straight rod moved at right angles across a magnetic field?
Model answer
The free electrons in the rod travel with it through the field, so each feels a force Bqv directed along the rod. They gather at one end and leave the other end positive, so a potential difference appears between the ends.
2
Derive the expression for the emf induced in a rod of length l moving with speed v at right angles to a field of flux density B.
Model answer
In a time t the rod sweeps out an area lvt, so the flux it cuts is Blvt. Dividing that change of flux by the time t gives an emf of Blv.
3
State the expression for the emf induced in a moving linear conductor, defining every symbol and its unit.
Model answer
The emf is E = Blv. B is the flux density in T, l the length of conductor in the field in m and v the speed at right angles to the field in m s⁻¹, giving an emf in V.
4
Which end of a moving rod becomes positive?
Model answer
The end towards which conventional current would be driven becomes positive. Fleming's right-hand rule finds it, with the first finger along the field and the thumb along the motion.
5
State Fleming's right-hand rule and say when it is used.
Model answer
Hold the thumb and first two fingers of the right hand mutually at right angles, with the First finger along the Field, the thuMb along the Motion of the conductor and the seCond finger giving the induced conventional Current. It applies to a conductor moved through a field, not to a current placed in one.
6
A rod 0.80 m long moves at 12 m s⁻¹ at right angles to a field of 0.050 T. Calculate the emf induced across it.
Model answer
The emf is E = Blv = 0.050 × 0.80 × 12 = 0.48 V. Dividing 0.48 V by 0.050 T and by 0.80 m returns a speed of 12 m s⁻¹.

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