Electric Potential of Conducting Sphere: Charge & Charge Density

In summary, using the equation v = kq/r, where V is the potential, r is the radius, and k is a constant, the charge on the surface of a conducting sphere with a radius of 0.21 m and a potential of 290 V is 5.5 x 10^11 C. To find the charge density, the equation \sigma = q/SA can be used, where \sigma is the charge density and SA is the surface area of the sphere. The surface area of a sphere is 4\pi r^2. After plugging in the values, the calculated charge density is 9.9 x 10^11 C/m^2. However, this value is incorrect as
  • #1
popo902
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0

Homework Statement



What are (a) the charge (in C) and (b) the charge density on the surface of a conducting sphere of radius 0.21 m whose potential is 290 V (with V = 0 at infinity)?

Homework Equations



v = kq/r
[tex]\sigma[/tex] = q/SA
SA of a sphere = 4[tex]\pi[/tex]r^2

The Attempt at a Solution


so this is what i did
i used the first equation and solved for q = Vr/k
i plugged in the numbers
v= 290, r is the same as the radius because its only the surface r = 0.21,
k = 1/(4[tex]\pi\epsilon[/tex])
I got 5.5e11
the right answer is 6.8E-9

Then for the charge density,
i put the numbers in too
but this is also wrong for sure because it uses my q value
I got 9.9e11
the right answer is 1.2e-8

I don't know how i got that far off :frown:
 
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  • #2
How did you get that value for q?

ehild
 
  • #3
yeh sorry i realized i divided by 1/k istead of multiplying by k/1 :S
 

FAQ: Electric Potential of Conducting Sphere: Charge & Charge Density

What is the electric potential of a conducting sphere?

The electric potential of a conducting sphere is the potential energy per unit charge at any point on the surface or inside the sphere. It is measured in volts (V) and is a function of the distance from the center of the sphere.

How is the electric potential of a conducting sphere calculated?

The electric potential of a conducting sphere can be calculated using the formula V = kQ/r, where k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance from the center of the sphere.

What is the relationship between charge and electric potential in a conducting sphere?

The electric potential of a conducting sphere is directly proportional to the charge of the sphere. This means that as the charge increases, the electric potential also increases, and vice versa.

What is charge density in relation to electric potential of a conducting sphere?

Charge density is a measure of how much charge is present per unit volume of a material. In the context of a conducting sphere, charge density refers to the distribution of charge on the surface or within the sphere that affects the electric potential at any given point.

How does the electric potential of a conducting sphere change with changes in charge density?

The electric potential of a conducting sphere is inversely proportional to the charge density. This means that as the charge density increases, the electric potential decreases, and vice versa. This is because a higher charge density means that the charges are closer together, resulting in a stronger electric field and a lower electric potential.

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