A thin, uniformly charged spherical shell has a potential of 757 V on its surfac

Question

A thin, uniformly charged spherical shell has a potential of 757 V on its surface. Outside the sphere, at a radial distance of 21.0 cm from this surface, the potential is 474 V. Calculate the radius of the sphere. 35.17 cm Determine the total charge on the sphere. 2.96x10-8 C What is the electric potential inside the sphere at a radius of 2.0 cm? Calculate the magnitude of the electric field at the surface of the sphere. 2.15X103 V/m If an electron starts from rest at a distance of 21.0 cm from the surface of the sphere, calculate the electron's speed when it reaches the sphere's surface. 9.97x106 m/s

Explanation / Answer

Here ,

let the charge on the sphere is Q

for radius ,r = 35.17 cm

at the surface

as Potential = k * Q/r

757 = 9*10^9 * Q/(0.3517)

Q = 2.96 *10^-8 C

the total chrage on the surface is 2.96 *10^-8 C
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as the potential inside the sphere is given as

V = k *Q/(2*R ) (3 - r^2/R^2)

for r = 2 cm

V = 9*10^9 * 2.96 *10^-8 /(2 * 0.3517) * (3 - (0.02/.3517)^2)

V = 1135 V

the potential at 2 cm from the sphere centre is 1135 V

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for the electronc field

E = 9*10^9 * 2.96 *10^-8 /(0.3517^2)

E = 2152.4 N/C

the electric field is 2152.4 N/C

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let the speed of electron is u

Using work energy theorum

0.5 * 9.1 *10^-31 * u^2 = 1.602 *10^-19 *(757 - 474)

u = 9.98 *10^6 m/s

the speed of the electron at the surface of sphere is 9.98 *10^6 m/s

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