Question

A piece of plastic is uniformly charged with surface charge density n1.

1. The plastic is then broken into a large piece with surface charge density n2.
2. A small piece with surface charge density n3
3. Rank in order, from largest to smallest, the surface charge densities n1 to n3.
A. n1>n2>n3.
B. n1>n2=n3.
C. n1=n2=n3.
D. n2=n3>n1.
E. n3>n2>n1.

Answer 1

Breaking a uniformly charged piece of plastic does not change the surface charge density for any of the pieces, hence n1=n2=n3.

Step-by-step explanation:

When a piece of plastic is uniformly charged, breaking it into pieces does not change the surface charge density on each piece. The surface charge density (σ) is defined as the charge per unit area. Since the charges were uniformly spread out on the original piece, they will remain so on any piece after breaking, regardless of its size. Thus, if the original surface charge density is n1, the large piece with surface charge density n2, and the small piece with charge density n3, all pieces will still have the same surface charge density as the original plastic.

The correct answer is therefore C. n1=n2=n3.

Answer 2

E

Step-by-step explanation:

Since the definition of density is mass per unit volume, the surface density has to do with the area of the surface.

If a piece of plastic is uniformly charged with surface charge density n1, that means that the charge density will be charged per unit area.

The magnitude of the charge depends on the surface areas.

As the surface areas reduce, the magnitude of the charge will be increasing.

Ranking in order, from largest to smallest, the surface charge densities n1 to n3, the correct option will be option E which is n3>n2>n1