A point charge q1 = 4.10 nC is located at the x-axis at x = 2.00 m, and a second point charge q2 = −6.30 nC is on the y-axis at y = 1.00 m. What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with the following radius? (a) 0.500 m N⋅m2 /C (b) 1.50 m N⋅m2 /C (c) 2.50 m N⋅m2 /C
![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)
