Eduqas Physics for A Level Year 2: Student Bk

97 2.6 Electrostatic and gravitational fields of force Answers g = GM E (3.7 × 10 8 m) 2 – GM S (1.51 × 10 11 m) 2 towards the Earth = 6.67 × 10 –11 N kg 2 m –2 5.97 × 10 24 kg (3.7 × 10 8 m) 2 – 1.99 × 10 30 kg (1.51 × 10 11 m) 2 = −2.91 × 10 −3 N kg −1 towards the Earth i.e. 2.91 × 10 −3 N kg −1 towards the Sun. and V = – GM E 3.7 × 10 8 m + – GM S 1.51 × 10 11 m which similarly leads to V = −8.80 × 10 8 J kg −1 . 2.6.8 Gravitational field lines and equipotentials Allowing for the different type of field, gravitational field lines (see Terms and definitions ) have the same properties as electric field lines (Section 2.6.5) except that they come from infinity and end on anything with mass. Equipotential surfaces are, again, pretty much self-explanatory. Note that in Fig. 2.6.22 the equipotential surfaces are spheres of less and less negative potential as their radii increase. Fig. 2.6.23 (a) shows the pattern of field lines and equipotentials for two spherically symmetric bodies of unequal mass. It is identical to the electric field pattern for two negative point charges such that Q 1 Q 2 = M 1 M 2 . Figs 2.6.23 (b) and (c) are sketches of the field strength and potential along the line AB (the x direction, say). Note in particular the point between M 1 and M 2 at which the field strength is zero. It corresponds to a local maximum in the potential, in accordance with the relationship g = – ∆ V ∆ x = − Gradient of tangent of V – x graph A gravitational field line is a line whose direction at each point along it is the direction of the gravitational field at that point. An equipotential surface in a gravitational field is an imaginary surface on which all points are at the same potential. Terms & definitions Fig. 2.6.22 Field lines and equipotentials for a small body with mass A B M 1 M 2 (a) (b) (c) g to right g to left 0 ¾ D ¼ D 0 Fig. 2.6.23 Field due to spheres of unequal mass 2.6.21 Self-test In Fig. 2.6.23, the centres of M 1 and M 2 are distance D apart. Calculate the ratio M 1 M 2 from the additional data in the figure.