DHS 15 Electric Fields (Notes & Tutorial)

Dunman High School (Senior High Physics) 9749 Physics (2025) Topic 13: Electric Fields Page 1 of 39 Guiding Questions  What is electric charge? How do charges interact?  What do field lines represent? Do field lines represent similar things for gravitational fields and electric fields? Content  Concept of an electric field  Force between point charges  Electric field of a point charge  Uniform electric fields  Electric potential Learning Outcomes Students should be able to: Concept of an electric field (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 Electric force between point charges (d) recall and use Coulomb's law in the form 2 1 2 4 oF Q Q r  for the electric force between two point charges in free space or air Electric field of a point charge (e) recall and use 24 oE Q r  for the electric field strength of a point charge in free space or air Uniform electric fields (f) calculate the electric field strength of the uniform field between charged parallel plates in terms of potential difference and 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 Electric potential (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 4 oV Q r  for the electric potential in the field of a point charge, in free space or air. 9749 H2 Physics Topic 13 Electric Fields Year 6 (2025) DUNMAN HIGH SCHOOL

Dunman High School (Senior High Physics) 9749 Physics (2025) Topic 13: Electric Fields Page 2 of 39 (c) recognise the analogy between certain qualitative and quantitative aspects of electric field and gravitational field. 1. Analogy between electric field and gravitational field field: electric gravitational force [discussed in detail in learning outcome (d)]  2 1 r  1 2 2e Q QF k r      [Coulomb’s law]  between two point charges Q1 and Q2  SI units: N  a vector  2 1 r  2'g MmF k r      [Newton’s law of gravitation]  between two point masses M and m  SI units: N  a vector force acts on: object with charge only object with mass only field strength [discussed in detail in learning outcome (e)] FE q (definition)  2 1 r  1 2 QE k r       due to a point charge Q1 [in a vacuum (free space) or air]  SI units: N C−1 (point charge) or V m−1 (parallel plate)  a vector Fg m (definition)  2 1 r  2' Mg k r       due to a point mass M  SI units: N kg−1  a vector field strength depends on medium? Yes, 0 1 4k   .  : dielectric constant of material; for vacuum, 1  ; for air (1 atm), 1.00059  0 : permittivity of free space = 8.85  10−12 C2 N−1 m−2 (or F m−1) No, 'k G . field generated by: charge mass example of uniform field: between charged parallel plates having a p.d. across them on surface of the Earth potential [discussed in detail in learning outcome (k)] WV q  1 r  1 0 1 4 QV r           sign depends on type of point charge  V is zero at infinity  SI units: J C−1  a scalar W m   1 r  MG r        sign is always negative   is zero at infinity  SI units: J kg−1  a scalar potential energy of two point charges or masses  1 r  1 2 0 1 4 Q QEPE r           r : distance between Q1 and Q2  positive (negative) if Q1 and Q2 have the same sign (opposite signs)  SI units: J  a scalar  1 r  MmGPE G r        r : distance between M and m  it is always negative  SI units: J  a scalar relationship between field strength and potential dVE dr  dg dr  

Dunman High School (Senior High Physics) 9749 Physics (2025) Topic 13: Electric Fields Page 3 of 39 (d) recall and use Coulomb's law in the form 2 1 2 0 4F Q Q r  for the force between two point charges in free space or air. 2. Coulomb’s law Coulomb’s law states that the electric force F acting between any two point charges Q1 and Q2 is directly proportional to the product of the charges and inversely proportional to the square of their separation r. The direction of the force is along the line joining the two point charges. i.e. 1 2 2 QQF r  1 2 2 Q QF k r  1 2 2 04 Q QF r  where the constant of proportionality 01 4k  = 9.0  109 N m2 C−2 The permittivity of free space, 0 = 8.85  10−12 C2 N−1 m−2 (or F m−1) (given in data list) Note: This relation is applicable only to point charges. For practical purposes, two charged bodies can be treated as point charges if they are separated far apart such that the size of each of the charged bodies is negligible compared to their separation. Example 1 Two point charges Q (+2.0 C) and q (+1.0 C) are separated by a distance of 3.0 m. (a) Determine the magnitude and direction of the force of Q on q, Fq. (b) Determine the magnitude and direction of the force of q on Q, FQ. (c) If q is negatively charged with twice its original magnitude, determine the new magnitude and direction of the force of Q on q, Fq’. Solution (a) Since both charges are positive, Fq is repulsive and is directed away from Q, along the line joining Q and q. Using Coulomb’s law, 6 6 2 12 2 0 1 ( 2.0 10 )( 1.0 10 ) 4 4 (8.85 10 )(3.0) q QqF r           = +2.0 × 10–3 N (b) Fq and FQ forms a Newton’s 3rd law action-reaction pair, thus | | | |Q qF F = 2.0 × 10–3 N FQ is directed away from q, along the line joining q and Q. (c) Since both charges are oppositely charged, the force is attractive. Fq’ is directed towards Q, along the line joining q and Q. Using Coulomb’s law, 6 6 2 12 2 0 1 ( 2.0 10 )( 2.0 10 )' 4 4 (8.85 10 )(3.0) q QqF r           =  4.0 × 10–3 N The magnitude of the force is 4.0 × 10–3 N. +q +Q FQ Fq 3.0 m Q q -q +Q Fq’

Dunman High School (Senior High Physics) 9749 Physics (2025) Topic 13: Electric Fields Page 4 of 39 (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 3.1 Electric Field: concept of a field revisited A field of force 1 is a region of space within which there could be a non-contact force acting on an object placed in that field. Specifically, an electric field is a region of space within which there is an electric force acting on a charged object placed in that field. Electric field strength at a point in an electric field is defined as the electric force per unit positive charge exerted on a small test charge2 placed at that point. Mathematically, electric field strength E at a point can be expressed as FE q where F is the electric force acting on the charge (unit: newton, symbol: N) q is the electric charge (unit: coulomb, symbol: C). Notes:  F qE  Electric field strength, E is a vector and has units: N C−1 (or V m−1).  The direction of electric field strength at a point in an electric field is the same as that of the force acting on a small positive test charge, q placed at that point.  Since there are two types of electric charge (positive and negative)