A thin, uniformly charged spherical shell has a potential of 666 V on its surfac

Question

A thin, uniformly charged spherical shell has a potential of 666 V on its surface. Outside the sphere, at a radial distance of 25.0 cm from this surface, the potential is 373 V. The radius of the sphere is 31.83 cm. The total charge on the sphere is 2.36x10^-8 C. What is the electric potential inside the sphere at a radius of 1.0 cm? Calculate the magnitude of the electric field at the surface of the sphere. If an electron starts from rest at a distance of 25.0 cm from the surface of the sphere, calculate the electron's speed when it reaches the sphere's surface.

Explanation / Answer

**********************

Note that wherever inside the sphere, the potential is the same as the surface.

Thus, at r = 1.0 cm,

V(1.0 cm) = 666 V   [ANSWER, field at 1.0 cm]

***********************

At the surface of the sphere, the E-field is

E = kQ/R^2

k = 8.99E9 N m^2/C^2
Q = charge of the sphere = 2.36E-8 C
R = radius of the sphere

= 2094 N/C   [ANSWER, field at the surface]

**********************

Note that

KEf - KEi = delta(PE) = q(Vf - Vi)

As Vf = 666 V, Vi = 373 V, q = 1.602E-19 C, KEi = 0,

KEf = 4.694E-17 J

As KE = 1/2 m v^2 ---> v = sqrt(2KE / m), m = 9.11E-31 kg,

v = 1.015*10^7 m/s [ANSWER, electron's speed]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.