A non-conducting sphere, of radius R, is given a charge of -Q. The charge is dis

Question

A non-conducting sphere, of radius R, is given a charge of -Q. The charge is distributed through the sphere following a charge density of rho(r) = a squareroot r. Find the expressions for the electric field inside and outside the sphere (as functions of radius from the center of the sphere) and describe the direction of the electric fields. If IQI = 3 nC and R = 50 cm, what maximum speed would an electron (released from rest near the surface of the sphere) reach? What is the electric potential at the surface of the sphere?

Explanation / Answer

From gauss's law
E*4*pi*r^2 = Q/epsilon
E = kQ/r^2

a) For r < R
dq at radius r
dq = (alpha)sqroot(r)*4*pi*r^2*dr
Q(r) = 2*alphs*4*pi*r^7/2 / 7
so E = k*Q(r)r/R^3

For r > R
E = k*Qo/R^2
Direction, towardds the centre of the sphere always
b) Potential at the surface of the sphere = kQ/R = 8.89*10^9*3*10^(-9)/0.5 = 53.34 V
PE = P*q = 1.6*10^-19*53.34 = 85.344*10^-19 J = 0.5*9.1*10^-31*v^2
v = 4330926.353 m/s
c) P = 53.34 V

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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