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# A thin uniform rod extends along z-axis from z= -d to z=d. The rod carries a positive charge Q uniformly distributed along its length 2d with charge density t=Q/2d.a) claculate the electric potential at a point z>d along z axis.b)What is the change in potential energy if an electron moves from z=4d to z=3d.c)if the electron started out at rest at the point z=4d what is its velocity at z=3d.?

Arun Kumar IIT Delhi
7 years ago
Let the length of wire be limited but the point in consideration
make angle theta2 with lower end end and perpendicular distance
and angle theta1 with upper end and perpendicular distance.
x be the perpendicular distance.

Then
$E_x=\lambda [sin(\theta_1)+sin(\theta_2)]/4\pi \epsilon x,E_y=\lambda [cos(\theta_1)-cos(\theta_2)]/4\pi \epsilon x \\\\=>here \\sin(\theta_1)=d/\sqrt{d^2+x^2} \\sin(\theta_2)=d/\sqrt{d^2+x^2} \\=>E_y \to 0 \\=>E_x=\lambda 2*d/(\sqrt{d^2+x^2}*4\pi \epsilon x)$
a)replace x with z
b)integrate from 4d to 3d its easy given E is already found.
c)equate mode of value in b to 1/2 mv2

Thanks & Regards
Arun Kumar
IIT Delhi