Question

Select Tru or False.

1. A conducting sphere with charge Q at equilibrium has zero E field inside it. The E field outside is the same as that of a point charge Q, E=keQ/r2. The potential outside it is the same as that of a point charge Q. V= keQ/r. (r is the distance to the center). The potential inside the conducting sphere is equal to the potential at its surface. V= keQ/R. (R is the radius of the sphere)

2. When a conductor is at equilibrium, if it has an empty cavity, the E field INSIDE the cavity mush be zero. The potential inside the cavity is a constant and equals to the potential of the conductor.

3. When a conductor is charged and reach equilibrium, the charges can only be on the surface, because the charges repel each other and can move freely in a conductor, so they would stop only when they reach the surface.

4. When a conductor is at equilibrium, the E field INSIDE is zero everywhere. So the potential inside is also zero.

5. A conductor at equilibrium has same potential throughout itself, both on the surface and inside.

6. When a conductor is at equilibrium, the E field on the surface must be perpendicular to the surface and has no components parallel to the surface, otherwise, free charges will flow on the surface, and it is no longer equilibrium.

7. Two conducting spheres with radius r₁ and r₂ and charges q₁ and q₂, respectively, are connected with a conducting wire. The one with more charge will have a higher potential.

8. On a conductor, the sharp parts have denser charge distribution and create stronger E field. When the E field is extremely strong, it can ionize air and cause discharge around it. That’s why the lightning rod was made sharp and pointy.

9. When a conductor is at equilibrium, the E field INSIDE is zero, so the potential inside is a constant everywhere, but may not be zero.

10. Two conducting spheres with radius r₁ and r₂ and charges q₁ and q₂, respectively. If they are connected with a conducting wire and at equilibrium, they have the same potential, hence, q₁ /r₁ = q₂ /r_2.
If r₁ < r₂, because q₁ /r₁ = q₂ /r_2, we know (q₁ /r₁)/(4pir₁) > (q₂/r₂)/(4pir₂),
hence, q₁ /(4pir₁²) > q₂/(4pir₁²). The smaller sphere has a large charge density. Because that the E field on the surface is equal to charge density over epsilon₀, E field is stronger on the surface of the smaller sphere.

11. A conductor at equilibrium has same potential on the entire surface and has zero potential inside.

12. Two conducting spheres with radius r₁ and r₂ and charges q₁ and q₂, respectively. If they are connected with a conducting wire and at equilibrium, they have the same E field value on their surfaces, hence, q₁/r₁² = q₂/r₂²_.

_13.A conducting sphere with charge Q at equilibrium has zero E field inside it. The E field outside it is the same as that of a point charge Q, E=k_eQ/r². (r is the distance to the center). This can be found by using a sphere Gaussian surface. For object of shapes other than a perfect sphere, this may not be true.

14. A charged conductor has same potential everywhere at equilibrium. The sharp spots with small radius of curvature have smaller charge density and weaker E field around than the flat parts with large radius of curvature.

Answer 1

1. TRUE.

2. TRUE.

3. TRUE

4. FALSE. Electric Field is negative gradient of potential which implies for electric field inside a conductor to be zero, the potential inside the conductor must be constant.