Help on conceptual potential and radii multiple choice

[physics100000]

help! on conceptual potential and radii multiple choice

Homework Statement

Two positively charged metal spheres of different radii are connected by a conducting wire. Which statement is true about them?

a. their potentials are the same
b. their charges are the same
c. their electric fields are constant everywhere
d. the charge on the smaller sphere is larger

Homework Equations

V= Q/R
change in V = -integral of E dr
V= ED

The Attempt at a Solution

a. i don't think its this because potential is based on radius and if the radius is different then the potential is not the same.
b. this could be true because if the two spheres are connected, then the charge will evenly distribute
c. i don't think this is true because electric fields is dependent on radius
d. this might be true because V= Q/R and so since R is smaller then V is larger so Q is larger too, being directly proportional.
Please help!

 

[anathema]

I can understand your confusion about this question. Let's break down each statement and see which one is true.

a. The statement says "their potentials are the same". This means that the potential (V) of both spheres is equal. As you correctly mentioned, potential is dependent on radius (R) and charge (Q). The equation V=Q/R shows that if the radius is different, the potential will also be different. Therefore, this statement is not true.

b. This statement says "their charges are the same". This means that the two spheres have equal charges (Q). As you mentioned, when two spheres are connected by a conducting wire, the charge will evenly distribute. This means that the total charge of both spheres will be the same. However, since the spheres have different radii, their individual charges will not be the same. Therefore, this statement is also not true.

c. This statement says "their electric fields are constant everywhere". Electric field (E) is also dependent on radius and charge, just like potential. Therefore, if the radii are different, the electric fields will also be different. Hence, this statement is not true.

d. This statement says "the charge on the smaller sphere is larger". This is the correct answer. As you mentioned, the potential is directly proportional to charge and inversely proportional to radius. This means that if the radius is smaller, the potential will be larger. Since the potential is the same for both spheres (as they are connected by a conducting wire), the smaller sphere must have a larger charge to compensate for its smaller radius.

I hope this explanation helps you understand the concept of potential and radii better. Keep up the good work in your studies!