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A spherical capacitor is formed from two concentric sphericalconducting shells separated by vacuum. The inner sphere has radius10.0 centimeters, and the separation between the spheres is 1.50centimeters. The magnitude of the charge on each sphere is 3.30nanocoulombs.1)What is the magnitude of the potential difference DeltaV between the two spheres?2)What is the electric-field energy stored in the capacitor?

Respuesta :

muhammadjonedkhattak

Answer:

Δ V = 38.74 V, W= 6.39 × 10 ⁻⁸ J

Explanation:

Given: Let inner Sphere Radius r1 = 10.0 cm = 0.1 m

separation d = 1.50 cm = 0.015 m

so the radius of outer sphere will be 0.1 + 0.015 = 0.115 m =r2

charge Q = 3.30 nC= 3.30 × 10 ⁻⁹ C

K= 9.0 x 10⁹ N • m² / C²

To Find: Δ V= ? and W=?

Solution:

1) we know that   Δ V = K Q / (1/r1 - 1/r2)

Δ V = 9.0 x 10⁹ N • m² / C² × 3.30 × 10 ⁻⁹ C / (1/0.1 - 1/0.115)

Δ V = 38.74 V

2) W = VQ/2    

W=   1980 V  × 3.30 × 10 ⁻⁹ C /2

W= 6.39 × 10 ⁻⁸ J

okpalawalter8

We have that for the Question "1)What is the magnitude of the potential difference DeltaV between the two spheres?2)What is the electric-field energy stored in the capacitor?"

it can be said that

  • Magnitude of the potential difference = [tex]38.7 V[/tex]
  • Electric-field energy stored in the capacitor = [tex]6.39*10^{-8} J[/tex]

From the question we are told

The inner sphere has radius10.0 centimeters, and the separation between the spheres is 1.50centimeters. The magnitude of the charge on each sphere is 3.30nanocoulombs.

Generally the equation for the potential difference [tex]\delta V[/tex] is mathematically given as

[tex]\deltaV = kq \frac{(r_f- r_i)}{r_f r_i}\\\\= 8.99*3.30 * \frac{(0.015)}{0.100 * 0.115}\\\\= 38.7 V[/tex]

The equation for  the electric-field energy stored in the capacitor is mathematically given as

[tex]\frac{1}{2}QV \\\\= \frac{1}{2} * 3.30*10^{-9} * 38.7\\\\=6.39*10^{-8} Joules[/tex]

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https://brainly.com/question/23379286

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