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Electric Fields Year 13 Electrostatic force • Like charges repel, unlike charges attract • How does this force act if charges are not in contact? – An electric field exists Electric field lines • An electric field is a region where a charged body experiences an electrostatic force • Like gravitational fields, we can represent electric fields by field lines – Lines show the direction of the force experienced by a positive test charge – Lines never cross – The more lines, the stronger the field – Lines start and stop at charges (or ∞) • Experiment to see field patterns Electric field patterns Equipotentials • Equipotentials join points in a field at the same potential – No work is done moving along equipotentials • Equipotentials are perpendicular to field lines • Any conductor is an equipotential surface – Because charge is free to spread out (resourcefulphysics.org) TAP 406.3 Coulomb’s Law • e0 is called the permittivity of free space. • Permittivity is a property of a material that is indicative of how well it supports an electric field. • Different materials have different permittivities, and so the value of k in Coulomb’s law will change for different materials. Coulomb’s Law kq1q2 F 2 r • Inverse square law, like gravity • Attractive (-) or repulsive (+) force • Valid for point charges or charged spheres Worked example – – – – k = 1/ (4pe0) = 9.0 109 N m2 C-2 mass of an electron = 9.11 10-31 kg mass of a proton = 1.67 10-27 kg G = 6.67 10-11 N m2 kg-2 •What is the force of repulsion between two electrons held one metre apart in a vacuum? •What is the gravitational force of attraction between them? •By what factor is the electric repulsion greater than the gravitational attraction? •TAP 407.1 Electric field strength • A property of the field, not the test charge • Field strength is the Force felt by a unit charge F kq E 2 q r Potential energy • Zero electric potential energy defined at infinity • Have to do work to bring a charge +q a distance r from a charge +Q • Work is stored as electrical potential energy • If two charges are opposite, it takes work to separate them, potential energy is negative. – Must keep track of signs! +Q r P +q Infinity (∞) kQq EPE r Electrical potential • Potential is the potential energy per unit charge EPE kQ V q r – Units: J/C, or volts – A property of the field, not the charge experiencing the field dV • Field strength=-potential gradient E dr Potential around a positive charge Potential and electric field intensity E = - dV/dr Potential (V) High field intensity Low field intensity 16 8 4 2 2 4 8 (resourcefulphysics.org) 16 Distance (x) Charged conducting sphere • All charge resides on the outside of the sphere • Electric field inside=0 • Potential inside is constant Uniform electric field • Found between two parallel plates – Equally spaced field lines – Equally spaced equipotentials • F=EQ=ma – So a charge will experience uniform acceleration from one plate towards the other V V E x d d Accelerating charges 0V cathode +5 kV anode Electron beam • Electrons experience a force • Work done=QV (charge x pd between two points)=energy gained moving with field • Found in electron guns (CRTs) horizontal displacement : x vxt 1 2 vertical displacement : y at 2 F eV a m md Motion of a body under constant upward acceleration 16000 14000 12000 10000 8000 6000 4000 2000 0 0 20 40 60 80 Vx=3, ax=0, Vy(t=0)=0, ay=2. 100 120 Cathode Ray Tube (CRT) Robert Millikan Millikan’s oil drop experiment Millikan’s Apparatus Comparing electric and gravitational fields Electric and gravitational fields • Similarities – For point charges or masses, the variation of force with distance follows the inverse square law. – Both exert a force from a distance, with no contact. – The field strength of both is defined in terms of force per unit of the property of the object that causes the force (i.e. mass and charge). • Differences – Gravitational fields can only produce forces of attraction, whereas electric fields can produce attraction and repulsion. – Objects can be shielded from an electric field, they cannot however be shielded from a gravitational field – Electrostatic force is many orders of magnitude greater than gravitational force.