Eduqas Physics for A Level Year 2: Student Bk

98 Eduqas A Level Physics Year 2: Component 2 Summary of properties of electric and gravitational fields Electric fields Gravitational fields The electric field strength, E , at a point is the force per unit charge on a small positive test charge placed at that point. The gravitational field strength, g , at a point is the force per unit mass on a small test mass placed at that point The inverse square law for the force between two point electric charges takes the form: F = 1 4 π ε 0 Q 1 Q 2 r 2 which is Coulomb’s law The inverse square law for the force between two point masses takes the form: F = G M 1 M 2 r 2 which is Newton’s law of gravitation F can be attractive or repulsive F is attractive only E = 1 4 π ε 0 Q r 2 is the field strength due to a point charge in free space (a vacuum) or in air g = G M r 2 is the field strength due to a point mass The potential, V , at a point is the work done per unit charge in bringing a small positive test charge from infinity to that point The potential, V , at a point is the work done per unit mass in bringing a small test mass from infinity to that point For a point charge: V E = 1 4 π ε 0 Q r and for two point charges: U P = 1 4 π ε 0 Q 1 Q 2 r For a point mass: V g = – G M r and for two point masses: U P = – G M 1 M 2 r Note that all the above equations also apply outside spherically symmetric charges Note that all the above equations also apply outside spherically symmetric masses The change of potential energy of a point charge displaced in an electric field is given by: Δ U P = q Δ V E The change of potential energy of a point mass displaced in an gravitational field is given by: Δ U P = m Δ V g Field strength at a point is given by: E = − slope of the V E − r graph at that point Field strength at a point is given by: g = − slope of the V g − r graph at that point ε 0 = 8.854 × 10 –12 F m –1 But 1 4 π ε 0 ≈ 9.0 × 10 9 F –1 m is an acceptable approximation G = 6.67 × 10 –11 N m 2 kg –2