Electric Potential in an Insulating Sphere

In summary, the problem involves a uniformly charged insulating sphere of radius a = 4.3 cm with charge density ρ = -421 μC/m3 and a concentric uncharged spherical conducting shell with inner radius b = 14.6 cm and outer radius c = 16.6 cm. The first question asks for the x-component of the electric field at point P, located at a distance d = 31 cm from the origin along the x-axis, with an answer of -13130.92 N/C. The second question asks for the electric potential at the inner surface of the conducting shell, defined to be zero at infinity, and requires taking the integral from infinity to c and from c to b, which results
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Homework Statement


A solid insulating sphere of radius a = 4.3 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density ρ = -421 μC/m3. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 14.6 cm, and outer radius c = 16.6 cm.
h6_sphere1.png


1) What is Ex(P), the x-component of the electric field at point P, located a distance d = 31 cm from the origin along the x-axis as shown? I got the answer correct: -13130.92 N/C

2) What is V(b), the electric potential at the inner surface of the conducting shell? Define the potential to be zero at infinity.

I am having trouble with number 2. I only have one more chance to submit an answer for number 2 so I can really use some help.

Homework Equations


ΔV=-∫E*dr
E = kQ/r

The Attempt at a Solution


For number 2 I took the integral infinity to c ∫E*dr and from c to b (which I assumed to be 0 since it is the shell) and then to calculate the integral I got (k(Q(calculated in q1)+q(of inner sphere determined by density)/c). I got -7.119E14. What did I do wrong?
For my first try I did (kq(innersphere))/b and got the message " It looks like you have calculated the potential at the inner radius of the shell to be equal to the potential at r = c produced by the insulating sphere by itself. The conducting shell plays a role here. Go back to the definition of the potential to determine the answer." But I'm not quite sure what that means.
I have also just considered that it might be the answer to number 1 (if that would be the E for the region) divided by c. Does that make sense? I'm kinda confused and afraid to guess.[/B]
 
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  • #2
What is the total charge inside a spherical surface of radius R > c?
 

FAQ: Electric Potential in an Insulating Sphere

What is Electric Potential?

Electric potential is a measure of the potential energy per unit charge at a specific point in an electric field. It is also known as voltage and is measured in volts.

What is an Insulating Sphere?

An insulating sphere is a spherical object made of a material that does not conduct electricity. This means that electric charges cannot flow through the material, creating a barrier to the flow of electric current.

How is Electric Potential Calculated in an Insulating Sphere?

The electric potential in an insulating sphere can be calculated using the following formula: V = kQ/R, where V is the electric potential, k is the Coulomb's constant, Q is the charge on the sphere, and R is the radius of the sphere.

What Factors Affect Electric Potential in an Insulating Sphere?

The electric potential in an insulating sphere is affected by the charge on the sphere, the radius of the sphere, the distance from the center of the sphere, and the dielectric constant of the material the sphere is made of.

What is the Difference Between Electric Potential and Electric Field?

Electric potential is a measure of the potential energy per unit charge at a specific point in an electric field, while electric field is a measure of the force per unit charge at a specific point in an electric field. In other words, electric potential is a scalar quantity, while electric field is a vector quantity.

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