Question 1 Consider the four solid spheres in the figure. In each case the point P is at the same distance from the centre of the sphere. For the situations listed below, rank the spheres according to the magnitude of the electric field at point P, from the largest to the smallest. Indicate any ties. Motivate your answers clearly. (a) (c) (d) (a) The spheres are non-conducting and uniformly charged with the same charge density. (b) The spheres are non-conducting and uniformly charged with the same total charge. Answers: (a) c = d, b, a (b) a = b, c, d
![Question 2 Apply what you know about conservation laws to the following questions. (a) Two protons are held fixed on the y-axis at y = a and y = −a. You release an electron (mass me) on the x-axis at x = 2 a. What is the maximum speed the electron will reach? (b) An electron (mass me) and proton (mass mp) are held a distance r apart. They are released simultaneously and begin to accelerate towards each other. What is the electron's speed by the time the distance between the charges has halved? Answers: (a) vmax = [e2 ameπϵ0(1−15)]1 /2 (b) ve = [14πϵ02 e2 mpme(me+mp)r]1 /2 Question 3 (a) Show that the electric field inside a solid charged sphere with a uniform charge density of ρ is E→(r→) = ρr→/(3ϵ0). Here r→ is a position vector relative to the centre of the sphere. Use known results for spherically symmetric charge distributions. (b) Suppose a spherical cavity is hollowed out of the sphere. The centre of the cavity is at position a→ relative to the centre of the sphere. Derive an expression for the electric field inside the cavity. You should find that it is perfectly uniform. Hint: Use your result in (a) together with the superposition principle.](https://www.doubtrix.com/uploads/editor/9839175511KTRtNuwhVd.jpg)
