© John Parkinson 1

2 Electric Field "An electric field is a region in which charged particles experience a force" ELECTRIC FIELD +Q FORCE -Q FORCE Lines of force show the direction of the force felt by a positive charge

3 THE DENSITY OF THE FIELD LINES IS A MEASURE OF THE STRENGTH OF THE FIELD - + Field lines start and end on charges

4 This is defined as the force per unit [+ve] charge acting at a point in the field. ELECTRIC FIELD STRENGTH E UNITS = ? N C -1 Hence the force on a charge of Q coulombs in the diagram above is given by : +Q F = E Q IT IS A VECTOR

5 Simply Potential [i.e. the volts] measures the energy of each coulomb of charge. Electric potential, V 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. Potential only depends on the charge causing the field and is a scalar Hence the energy of Q coulombs of charge at a point, where the potential is V volts is given by W = QV

6 +Q A point charge or a charged sphere produces a radial field Lines of Equipotential V These are perpendicular to the field lines FIELD PATTERNS At any point the field strength equals the potential gradient

7 +Q Field & Potential due a point charge or charged sphere At a distance r from the charge E is a vector V is a scalar

8 FIELD PATTERNS Oppositely charged parallel plates produce a uniform field between the plates Evenly spaced equipotentials – so it’s a uniform field. Equipotentials

9 V Volts d metres The field is uniform Hence the potential gradient  V/  r is uniform Hence It follows that E has units of N C -1 or V m -1

10 Electric Potential Contours (energy levels) -Q +Q 0 V -100 V 200 V 300 V 400 V 100 V -200 V -300 V This is analogous to climbing [and falling down] gravity hills QUESTION How much energy is required to move a +0.5 C charge from A to B? A B The potential difference  V = V B – V A = 200 – (- 100) = 300 Volts W = Q  V = 0.5 x 300 = 150 J

11 Motion of Charge Initially Moving Perpendicularly to an Electric Field e.g. an electron in an oscilloscope beam E x y -- vHvH V H is the initial horizontal velocity and REMAINS CONSTANT - Like a projectile !! For the vertical motion u = 0, so For the horizontal motion, x = V H t Hence which is a PARABOLA where m = mass of the particle and F = EQ

12 Gravitational FieldElectric 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 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 Comparing Gravitational and Electric Fields