2.1.1 – 2 Electric Fields An electric field is the region around a charged object where a force is exerted on a charged object. the force exerted on a pair of charged objects is proportional to the product of their charges and inversely proportional to the square of the distance of separation. Coulombs law states that the force exerted on a pair of charged objects is proportional to the product of their charges and inversely proportional to the square of the distance of separation. ie F = kQ 1 Q 2 r 2 r 2

F = kQ 1 Q 2 r 2 This is called the Electric Field Strength E = F/q Electric Field Strength E is the force exerted on a unit charge (one coulomb) placed in an electric field unitsNC -1 vector quantity It’s units are NC -1, and it is a vector quantity like gravitational field strength If we consider how one of the charged (Q 1 ) objects will affect any other charge brought near it we need to consider the force it will exert on just one coulomb of charge and then scale it accordingly. Ie from coulombs law this would be F/Q 2

Electric field strength will decrease as we move further away from the charge producing the field E  1/r 2 The value of the Electric field strength will decrease as we move further away from the charge producing the field according to the inverse square law E  1/r 2 (4  ) r 2 E = 1. Q (4  ) r 2 F = 1. qQ We already know that the force exerted by charged objects depends on the size of the charges and their separation as well as the substance separating them, therefore according to Coulombs law…… Qq E = F/q Therefore if the charge we place in the field caused by Q is q then since E = F/q it will experience a field strength of r 2 r 2 F = k qQ r2 r2 r2 r2 E = k Q 1 = k (4  ) If 1 = k (4  )

Electric Field Strength in uniform fields

Circular motion of charged particles in electric fields When an atom such as hydrogen, causes an electron to orbit around the outside, it does so because of the electrostatic force between the two charges. This can happen in radial fields and uniform fields as in the fine beam tube! * m Therefore electrostatic force = centripetal force kqQ = mv 2 kqQ = mv 2 r 2 r r 2 r v 2 = kqQ And so v 2 = kqQ mr mr Putting in all the relevant data gives us an orbital speed of 1.6 * 10 6 ms -1

Uniform Electric Fields uniform central region. As seen in the semolina & olive oil demonstration we know that the field between two parallel plates is uniform in the central region. uniform field field lines are parallel constant distance apart. In a uniform field the field lines are parallel and a constant distance apart. electric field strength varies very little The electric field strength varies very little

Work done in an electric field Whenever a force causes an object to move in the direction of the force work is said to be done. Therefore if an electric field exerts a force on a charged object it must be doing work. As we know work done = force * distance moved in the direction of the force W = F  x W = QV As we learned in Module 2 W = QV when a charge is moved through a p.d. work is done and therefore QV = F  x

V  x We could therefore prove that the voltage V is proportional to the distance moved  x, since the charge moving and the force depends on the the charges and the distance from it. So for a uniform field we end up with lines where the potential of that point and all points along it are equal. Just like contour lines on a map, joining points of equal height, which is how we described potential in module 2 when talking about mountains. electric field equipotential lines Therefore the electric field also has contour lines or equipotential lines where the same amount of work would be done if you moved a unit charge to any point on that line from a starting point. no work is done along an equipotential line However, no work is done (energy gained or lost) by moving a charge along an equipotential line just like E p when moving around a mountain on a contour line!

Since E=F/Q E = V/x measured in Volts/metre We get E = V/x measured in Volts/metre Electric Field Strength is the potential gradient for the field. Therefore the Electric Field Strength is the potential gradient for the field. if you increase the PD there will be a larger force exerted If the electric field strength is large the force exerted on the charged objects in the field will also be large. Ie if you increase the PD there will be a larger force exerted If you move the plates closer together the potential gradient will be steeper and therefore the Electric field strength so greater forces will be exerted.

Electric Field Strength in Radial Fields +Q equipotential This diagram shows how lines of equipotential exist similarly to contour lines on a map – Same energymove a charged objectany point on the line Same energy needed to move a charged object to any point on the line No energy needed to travel around the line No energy needed to travel around the line radial fieldAround a point charge we have a different field pattern known as a radial field

2kNC -1 A charge of 20nC will produce an electric field around it whose Electric field strength will decrease as you move away from it as shown. Check the calculations! + 30cm 20cm 10cm 4.5kNC -1 18kNC -1 These values can be seen to obey the inverse square law as shown in the graph.

from positive to negative! The shape of electric fields depends on the charged object(s) producing them. If we are talking about a single point charge, the field is radial. If we think of other objects they can be modelled on magnetic fields, remembering the field lines run from positive to negative! Isolated charge Unlike charges Like charges What would the fields look like for the situations above??

+Q If the charge was negative the field lines would point inwards. electric field strength decreases as you move away from the charge As you can visualise from the field lines – they get further apart as you move out from the centre – the electric field strength decreases as you move away from the charge The decrease obeys the inverse square law E = kQ/r 2 The decrease obeys the inverse square law since E = kQ/r 2 Separation Electric Field Strength field linesdirection of the force experienced by a positive charge placed in the field. The field lines indicate the direction of the force experienced by a positive charge placed in the field. E  1/r 2 Or E  1/r 2