Electric Field of a Charged Spherical shell

In summary, a solid conducting sphere and a conducting spherical shell are concentric with charges of 6.70 µC and -3.50 µC respectively. The electric field at a radius of 3 cm from the center is found by using the equation E = 3.2 µC / (4 * 3.14 * 8.85 * 10^-12 * 0.03^2) = 4.51 * 10^10 N/C. Similarly, at a radius of 7 cm, the electric field is E = 3.2 µC / (4 * 3.14 * 8.85 * 10^-12 * 0.07^2) =
  • #1
SamTsui86
31
0

Homework Statement



A solid conducting sphere of radius 2.00 cm has a charge 6.70 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a charge -3.50 µC. Find the electric field at the folowing radii from the center of this charge configuration.

a) r = 3 cm
b) r = 7 cm

Homework Equations



E = Q(inside) / (4 * pie * Eo * r^2)

Eo = 8.85 * 10^ -12

The Attempt at a Solution



Q(inside) is just 6.7 uc - 3.5 uc = 3.2 uc

I just plug in r to the equation to solve for E

It's wrong, please give me some hints. Thank You
 
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  • #2
that Q inside you calculated...

would you that value of Q in both questions??


remember enclosed charge
 
  • #3
Gauss's Law: [tex]\int_\text{closed surface} \vec E. d\vec S = q_\text{enclosed}/\epsilon_0[/tex]
 
  • #4
Ohh I understand it now, thank you very much
 

1. What is the formula for the electric field of a charged spherical shell?

The formula for the electric field of a charged spherical shell is E = kQ/r², where k is the Coulomb's constant, Q is the charge of the shell, and r is the distance from the center of the shell.

2. How does the electric field of a charged spherical shell vary with distance?

The electric field of a charged spherical shell follows an inverse square law, meaning that it decreases as the distance from the center of the shell increases. This relationship is represented by the formula E = kQ/r².

3. Why is the electric field inside a charged spherical shell zero?

Inside a charged spherical shell, the electric field is zero because the charges on the shell are distributed evenly, canceling out any electric field in the interior. This is known as the "shell theorem."

4. How does the electric field of a charged spherical shell differ from that of a point charge?

The electric field of a charged spherical shell is different from that of a point charge in that the electric field of a shell is constant at all points on the surface, while the electric field of a point charge decreases with distance. Additionally, the electric field inside a charged spherical shell is zero, while the electric field around a point charge is non-zero.

5. How does the electric field of a charged spherical shell affect objects placed within its field?

The electric field of a charged spherical shell can exert a force on any charged objects placed within its field. The direction and magnitude of this force depend on the charge and position of the object relative to the shell. Objects with the same charge as the shell will experience a repulsive force, while objects with opposite charges will experience an attractive force.

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