0 ELECTRIC FIELDS
Electric Field ELECTRIC FIELD FORCE FORCE 0 "An electric field is a region in which charged particles experience a force" +Q -Q Lines of force show the direction of the force felt by a positive charge
Electric Field Lines • Imaginary lines that are always drawn parallel to the direction of the electric field with arrows pointing in the direction of the field • These are called electric field lines and were introduced by Michael Faraday Michael Faraday, (22 September 1791 – 25 August 1867) was an English chemist and physicist (or natural philosopher, in the terminology of the time) who contributed to the fields of electromagnetism and electrochemistry.
+ - 0 Such a convenient aid for visualizing electric field patterns is to draw lines pointing in the direction of the field vector at any point ! • Field lines start and end on charges • The density of the field lines is a measure of the strength of the field
Field lines + Area S, Where is the density of field lines greatest?
2 Point Charges • Note: • number of lines on -2Q is twice as many as on +Q +Q -2Q
0 Other Electric Field Configurations
ELECTRIC FIELD STRENGTH E 0 +Q IT IS A VECTOR ELECTRIC FIELD STRENGTH E This is defined as the force per unit [+Ve] charge acting at a point in the field. UNITS = ? N C-1 Hence the force on a charge of Q coulombs in the diagram above is given by : F = E Q
Up • Down • Right • Left • Doesn’t move
QUESTION A. EA > EB B. EA= EB C. EA< EB
When released, the PEelec. is converted into Kinetic Energy. Remember the work-energy theorem? Work done on a system changes its energy! Work = ΔPEelec. 0 A Pair of Charges + +
0 Distance from charge is in radial direction. A Pair of Charges • Max. PEelec.: + + Electric field around a point charge! Does it look like Coulomb’s law? Look closely! F=kqq/r2 so PEelec= -Fd = - Work!
0 Field Potential • Field potential is defined as the potential energy of an object divided by the mass (or charge) of the object. • Let’s once again think about gravity and electricity!
Gravity “pulls” masses toward Earth. Mass has PEg when above the ground. Electric Field Pulls +q or pushes –q along Electric field lines. Charge has Pee when above “ground” Electrical “ground” is accepted as zero Volts 0 Energy associated with Force
Useful Analogies: 0 • Gravity Field • mass • g • PE= mgh • Electric Field • + Charge • E • PE=-qEd
0 Uniform Electric Field • Behaves very much like Earth’s gravitational field. • Energy depends on position!
The Electric Potential Moving an electric charge through space where electric fields are present can require work, since forces associated with the fields act on the charge. This work can be described as a change in potential energy. We introduce the new concept of “electric potential” to describe the amount of work needed to move a charge through a region with electric fields.
+ Electric potential, V 0 Electric potential is the electrical potential energy per unit charge (ie. per coulomb) at a point in a field. This is the work done per unit charge in bringing a small positive charge from infinity to the point. Simply Potential [i.e. the volts] measures the energy of each coulomb of charge. Hence the energy of Q coulombs of charge at a point, where the potential is V volts is given by W = QV Potential only depends on the charge causing the field and is a scalar
0 Changing Electric Potential Joules • Potential Difference Volts Coulomb
Lines of Equipotential V 0 FIELD PATTERNS +Q A point charge or a charged sphere produces a radial field These are perpendicular to the field lines At any point the field strength equals the potential gradient
+Q 0 Field & Potential due a point charge or charged sphere At a distance r from the charge E is a vector V is a scalar
+++++++++++++++++++++++++++++ -------------------------------------------------- 0 FIELD PATTERNS Oppositely charged parallel plates produce a uniform field between the plates Equipotentials Evenly spaced equipotentials – so it’s a uniform field.
d metres V Volts 0 The field is uniform Hence the potential gradient V/ris uniform Hence It follows that E has units of N C-1 or V m-1
0 Potential Difference in a Uniform Electric Field • E is constant • Like between parallel plates
100 V 200 V 300 V 400 V 0 V -200 V -300 V -100 V 0 Electric Potential Contours (energy levels) This is analogous to climbing [and falling down] gravity hills B +Q -Q A QUESTION How much energy is required to move a +0.5 C charge from A to B? The potential difference V = VB – VA = 200 – (- 100) = 300 Volts W = Q V = 0.5 x 300 = 150 J
0 Potential Difference between a point at infinity and a Point Charge Between 2 charges • Why at infinity? • As r becomes very large, V approaches zero!
Motion of Charge Initially Moving Perpendicularly to an Electric Field e.g. an electron in an oscilloscope beam. y - - - - - - - - - - E x -- + + + + + + + + + + + 0 vH VH is the initial horizontal velocity and REMAINS CONSTANT - Like a projectile !! For the vertical motion u = 0, so where m = mass of the particle and F = EQ For the horizontal motion, x = VH t which is a PARABOLA Hence
Summary We created this new concept, the electric field, because sometimes it is more convenient to work with. However, the electric field is real. There actually is energy stored in the field that can be detected by experiment.
Comparing Gravitational and Electric Fields Gravitational Field Electric Field Inverse Square Law Newton’s Law Inverse Square Law Coulomb’s Law Field Strength g = force per unit mass & is a VECTOR Field Strength E = force per unit charge & is a VECTOR Gravity Potential, Scalar & for Radial Field Electric Potential ,Scalar & for Radial Field Field strength = Potential Gradient Field strength = Potential Gradient Definition of potential Work done in bringing a unit mass from infinity to the point in the field Definition of potential Work done in bringing a unit charge from infinity to the point in the field Potential Energy Potential Energy
Electrostatics: • Force - Coulomb’s Law A Vector law • The electric field. E The electric field is a vector field • Electric potential. A scalar -like work
Coulomb’s Law: The electrostatic force between two charged objects is proportional to the quantity of each of the charges and inversely proportional to the square of the distance between the charges. If both charges are negative, the force is also repulsive. If one is positive and the other negative, the force is attractive. If a system contains many charges, the net force (vector) on any one of them is the (vector) sum of the individual forces from the individual charges (superposition).
Electric potential Difference-Voltage The voltage (or electric potential) of a battery determines • how much work the battery can do on an electric charge. • how much net electric charge is in the battery. • how much electric field is around the battery.