EJC Physics H213 E Field - 1. Notes (full)

“Faraday Cage” demonstration at the Singapore Science Centre. An innocent audience-volunteer can often be found sitting unharmed inside the cage, as high-voltage, high-current electrical arcs sends lethal amounts of charges coursing down the metallic cage structure. Content • Concept of an electric field • Electric force between point charges • Electric field of a point charge • Uniform electric fields • Electric potential Learning Outcomes Candidates should be able to: (a) show an understanding of the concept of an electric field as an example of a field of force and define electric field strength at a point as the electric force exerted per unit positive charge placed at that point (b) represent an electric field by means of field lines (c) recognise the analogy between certain qualitative and quantitative aspects of electric field and gravitational field (d) recall and use Coulomb's law in the form 12 2 04 QF Q r= for the electric force between two point charges in free space or air (e) recall and use 2 04 QE r= for the electric field strength of a point charge in free space or air (f) calculate the electric field strength of the uniform field between charged parallel plates in terms of the potential difference and plate separation (g) calculate the forces on charges in uniform electric fields (h) describe the effect of a uniform electric field on the motion of charged particles (i) define the electric potential at a point as the work done per unit positive charge in bringing a small test charge from infinity to that point (j) state that the field strength of the electric field at a point is numerically equal to the potential gradient at that point (k) use the equation 04 V Q r = for the electric potential in the field of a point charge, in free space or air.

A “field” is a region in space where a force is experienced by an “entity” without contact. A mass experiences a force when placed in a gravitational field. Similarly, a charged particle experiences force when placed in an electric field. Forces are vector quantities so the direction has to be well-defined. The direction of an electric field is the direction of force on a positive charge, by convention and by definition. An isolated mass generates its gravitational field in the region surrounding the mass and it permeates all of space (“to infinity”). Similarly, a charged particle or a collection of charged bodies, generate electric field in the surrounding region, all the way to infinity. When an additional charge particle comes into this region, the additional charged particle interacts with the existing electric field and experiences an electric force. Specifically, the tangent at a point on the electric field line shows the direction of electric force that acts on a small stationary positive test charge if the charge is placed at that point and is free to move. The arrows on electric field lines point away from positive charges and towards negative charges. The figure on the left represents the electric field between 2 particles of equal but opposite charges. A small stationary positive test charge at the position marked by will experience an electric force directed to the right. What do you think is the direction of the electric force acting on a negative charge placed at the same position? An electric field is a region of space where an electric charge experiences an electric force electric field lines • start on positive charges • end on negative charges + An electric field line must clearly define the direction of force experienced by a positive charge at that location; therefore field lines must never intersect.

A positive charge placed in an electric field tends to move from a region of “higher (potential) energy” to a region of “lower (potential) energy”. 3 isolated point charges are shown above. X and Y are both positively charged. X has less charge than Y. Y and Z have equal magnitude of electric charges of opposite polarities. Individually, the electric fields weaken with increasing distance from the charges. Two positive charges of same magnitude. Unlike charges of different magnitude. Two negative charges of different magnitudes. A point positive charge and a negatively-charged flat plate. The electric field lines reach the flat plate at right-angles. Two identical parallel plates of opposite charge. The strength of the uniform electric field in -between is stronger when the plates are closer to each other. X Y Z - - - - - - - - - + + + + + + + + - - - - - - - + + + + + + + - direction of electric field lines is from region of higher electric potential to region of lower electric potential (within the same diagram) electric field strength is • stronger where electric field lines are closer together • weaker where electric field lines are further away from each other electric field lines are perpendicular to conducting surfaces

The units of E is: [N C−1] or [V m−1]. Electric field strength is a vector quantity and therefore undergoes vector addition. The two basic geometries for electric field are (i) radial electric field due to an isolated point charge and (ii) a uniform electric field in-between oppositely-charged parallel plates. electric field strength of a point charge in free space or air: 2 0 1 4 Q rE    =  electric field strength of uniform electric field between charged parallel plates: E V d=  (ΔV : potential difference, V+ – V−) The electric force EF experienced by an electric charge q at a point in an electric field E where E is the resultant electric field strength at that point. This is analogous to placing a mass m inside a gravitational field of field strength g, gF mg= . Coulomb’s Law states that the [type of force ] electric force between two point charges is [magnitude] directly proportional to product of the two charges and inversely proportional to the square of separation between the two charges Q r E E d Electric field strength E at a point in the field is [type of force] electric force [ratio] per unit positive charge [specifics] on a small positive test charge at that point EF qE=

12 2 0 1 4 QQ rF     = (Compare the above with the gravitational force between two point masses, m1 and m2 separated by a distance r) 12 2 mG mF r= The direction of the electric force acts along the line joining the two point charges. The electric force can be attractive between unlike charges , or repulsive between like charges (in comparison to gravitational force which can only be attractive). By Newton’s 3rd Law, the electric force that Q1 exerts on Q2 is equal in magnitude and opposite in direction to the electric force that Q2 exerts on Q1 i.e. 1 2 2 1 on on Q Q Q QFF =− 0 is a constant known as the permittivity of free space (vacuum) or air at 8.85  10-12 C2 N-1 m -2. By reference to electric field fields, for a point outside a spherical conductor, the charge on the sphere seems to act as a point charge at its centre because the electric field lines are perpendicular to the surface of sphere, radial pattern make field lines appear to originate from centre of sphere + Q1 r Q2 r m1 m2 F F

Example 1 By considering electric field strength and Coulomb’s Law, provide the expression describing the electric field strength generated by a single point charge. Solution: By Coulomb’s Law: 12 2 04 e QF Q r= Recall that electric field strength is the electric force per unit positive charge experienced by a small stationary positive test charge at that point. The field strength due to Q1 is