I just need part e and f. Thanks in advance Consider a thin disk of charge with
ID: 1613671 • Letter: I
Question
I just need part e and f. Thanks in advance
Consider a thin disk of charge with radius R, centered at r = 0 and z = 0 in a cylindrical coordinate system. The disk has a charge per unit area of sigma. In this problem we will examine the potential at points on the z axis, ie. r = 0. The problem is broken into small steps to make it easier for you to follow. The disk can be decomposed into a set of rings. The drawing above highlights one ring of radius r and thickness dr. What is the total charge in this ring? What is the potential of this ring for points on the z axis? Let's call this V_ring(z). Now integrate the potentials of all rings in the disk to find the potential of the disk, V(z). Use your V(z) to find E_z(z). A positive test charge q approaches the disk along the z axis. This test charge has mass m and initial speed V_ infinity when it is extremely far away. Find an expression for the minimum necessary for the particle to actually touch the disk. If your test charge moved infinitesimally off the z axis it would break the symmetry and be subject to an E_r component of the electric field. Can you use your expression for V(z) to find the E_r component in this case? If so, briefly describe how you would do it. If not, briefly explain why not.Explanation / Answer
In the previous parts you must have solved for the expression of Potential V(z) of the disk on z- axis and it must have been inversely proportional to the distance z.
The potential energy of a charge and the mentioned disk system is simply the charge q multiplied by potential of the disk V(z).
Now since there is no external force acting on the charge disk system so the total energy of the system is conserved.
At infinity , the system has zero potential energy but some amount of Kinectic energy = (1/2)* m* v2
As the charge moves closer to the disk the K.E reduces and the P.E increases.
So if the charge is to just touch the disk then you must equate the K.E and P.E such that the initial K.E is completely converted into final P.E.