A charge, q, is distributed non-uniformly over a disk of radius R. The charge di

Question

A charge, q, is distributed non-uniformly over a disk of radius R. The charge distribution is described by the expression sigma = br^2. a. What is the electric field at point p which is a distance y above the plane of the disk and on a line that passes through the disk's center? b. If a charge -q and mass m is place at p and released from rest, how fast is it traveling when it hits the disk? Your answer will be in terms of q, R, y and k_E. A charge, q, is distributed non-uniformly over a solid sphere of radius R. The charge distribution is described by the expression rho = br. Use Gauss' Law to: a. Determine the magnitude of the electric field at point p which is a distance A > R from the center. b. Determine the magnitude of the electric field at point p which is a distance B

Explanation / Answer

2a] By Gauss law, E = kQenclosed/A^2

Qenclosed = integral b r 4pi r^2 dr = b*r^4 = bR^4

E = k*bR^4/A^2

b] here charge enclosed will be bB^4

E= k*bB^4/B^2

= kbB^2 where k is coloumbs law constant.

1) take a ring of thickness dr and radius r,

Its charge dq = sigma *2pi r dr

=br^2 *2pi rdr

= 2pi b r^3 dr

E = integral dE

= integral y*k*dq/(y^2 +r^2) ^1.5

= integral y*k*2pi*b r^3 dr/(y^2 +r^2)^1.5

= y*k*2pi*b(r^2 +2y^2) /sqrt (r^2 +y^2)

If answer has to be written in terma of q, not b,

then q= integral br^2 2pi r dr

q= b*2pi r^4/4 or 2pib =4q/r^4

So E= (4q/r^4)*y*k* (r^2 +2y^2) /sqrt (r^2 +y^2)

B) This part can not be answered in given terms. It will required to include term m also.

v = sqrt (2KE/m)

Even if we find KE by finding potential, m has to be used for sure.

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