1.1. Two charged objects X and Y are made to circle a point O. X and Y are at a distance, d = 1.8 × 10⁻⁸ m and they have equal masses, where m = 1.7 × 10⁻⁹ kg as shown in Fig. 1.1.

The objects carry an equal but opposite charge, where the magnitude q = 3.2 × 10⁻¹⁹ C.

Fig. 1.1

Calculate the acceleration of X and Y.

1.2. Calculate the time required for the particles in part a) to make one complete orbit. 

1.3. A torque is experienced by particles X and Y from part a) when placed in an electric field of strength 6.5 V m⁻¹. The electric field acts perpendicular to the line between X and Y. 

Calculate the magnitude and explain the presence of the instantaneous torque when the particles are just starting to move in the electric field.

1.4. The particles X and Y in part a) are replaced with a gold nucleus $A79197u$ of radius 7.0 fm, and an alpha particle of radius 1.7 fm. They are circling point O with the same separation d and are no longer in an electric field. 

Show that the separation of the gold nucleus and the alpha particle is around 90 x 10⁻¹⁶ larger than the separation of particles X and Y.