RI Y6 Remedial E-field Soln

Raffles Institution Year 5-6 Physics Department 1 2024 Year 6 H2 Physics Remedial Chapter 13: Electric Fields Suggested Solutions 1 (a) EA = π − −− × ×× 19 12 3 2 4.8 10 4 (8.85 10 )(3.00 10 ) = 4.796 x 10–4 N C–1 EB = π − −− × ×× 19 12 3 2 1.60 10 4 (8.85 10 )(4.00 10 ) = 8.992 x 10–5 N C–1 Resultant electric field = −−×+× 42 52(4.796 10 ) (8.992 10 ) = 4.88 × 10–4 N C–1 (b) VA = πε − − −× × 19 3 ( 4.8 10 ) 4 (3.00 10 )o = –1.439 × 10–6 V VB = πε − − × × 19 3 (1.6 10 ) 4 (4.00 10 )o = 3.597 × 10–7 V V = VA + VB = –1.439 × 10–6 + 3.597 × 10–7 = –1.08 × 10–6 V 2 (a) The electric field strength at a point is defined as the electric force exerted per unit positive charge placed at that point. (b) Main features of drawing: 1. Arrows point from positive charge X to negative charge Y. 2. More field lines (nearly double) point towards the negative charge compared to the positive charge. 3. Asymmetry of the field lines between the two charges, with the ‘hump’ closer to the positive charge. Symmetry about the horizontal line joining the two charges. (c) (i) Distance TY = 220.20 0.10 0.03 0.173 cm−= = Force on T due to charge at Y, FY = ( )( ) ( ) 10 10 4 22 2 6 2 10 1 2 10 2 23 10 N4r 4 0 03 1 0 YT o o ..qq . .πε πε −− − − ×× = = × × 0.20 cm X Y

Raffles Institution Year 5-6 Physics Department 2 Force on T due to charge at X, FX = ( )( ) ( ) 10 10 4 22 2 3 2 10 1 2 10 3 45 10 N4r 4 0 10 1 0 XT o o ..qq . .πε πε −− − − ×× = = × × Magnitude of the net force acting on T, F = 2 24 4( 3.45 2.23 ) 10 4.11 10 N−−+ ×=× (ii) Direction of the net force on T is acting towards the top right hand corner. 3 (a) (i) The electric field strength at a point is defined as the electric force exerted per unit positive charge placed at that point. (ii) 1. Electric field strength inside both spheres is zero 2. There is a point between the spheres, where electric field strength is zero and the electric field strength of sphere A is positive at its surface (which means that the direction of the electric field is away from sphere A). (iii) The particle will move towards sphere B and oscillate about x = 8.0 cm 4 (a) (i) The electric field strength at a point is defined as the electric force exerted per unit positive charge placed at that point. (ii) ( ) 41 2 0 600 18750 1 88 10 N C3 20 10 VE .d. − − −−∆= = = = ×∆× (iii) ( )( ) 19 15 15 2 31 1 60 10 18750 3 293 10 3 29 10 m s9 11 10 net EFF ma qE .qEa ..m. − − − = = × = = = ×= ×× Assuming constant acceleration and using kinematics equation in the horizontal direction, ( ) 2 2 9 15 2 3 20 10 4 41 10 s3 293 10 1 2 2 s . . at t . ut s a − − = + = = × = ×× T FResultant FX FY X Y

Raffles Institution Year 5-6 Physics Department 3 5 (c) (i) Shows arrows from + to – plates on all the given lines (ii) Surface of constant p