1. Consider a ring of charge with radius R and uniform charge per unit length λ where > 0. A negative point charge -q with mass m is constrained to lie on the axis passing through the ring's symmetry axis. The point charge is located a very, very small distance from the center of the ring. Show that the point charge approximately undergoes simple harmonic motion and find the corresponding frequency. Hint: show that the force on the point charge is approximately very similar to Hooke's law. You'll need to first find the electric field of the ring along it's symmetry axis.

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A hollow conducting spherical shell with inner radius "a" and outer radius "b" carries total charge +3q. A point charge +2q is placed at the center of the hollow shell a) Find the induced charges on the surfaces ra and rib. b) Find the work done by the electric field to move a proton (charge q) from rea to r=3b.

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You Answered Correct Answer A line of charge is placed along the negative x axis from x=-0.4m to x=0. The charge is uniformly distributed with linear charge density 3.06pC/m. A proton is released from rest at a point on the positive x axis 2.53m. When the proton has a speed of 472.1m/s, how far will it have moved (in m}? 1.0975 margin of error +/-1%

4.) Figure Q.2 (b) shows a cylindrical structure with length of 50 m. The inner and the outer surface are separated by free space and located at r = a and r = b respectively. The inner and outer surface of the structure contain a total charge of +1pC and -1pC, respectively. An infinitely long line charge with line charge density of +1pC/m is introduced along the axis of the structure. Given that a = 1 mm and b = 2 mm. +pa C/m? -Рь С/m? Figure Q.2(b) i. Calculate +pa and -pp at radius a and b respectively ii. Find D and E in all regions iii. Sketch graph |D| versus r

A water molecule with any spatial orientation is placed nearby a spherical distribution of charges Q. Describe the dynamic behavior (rotation and translation) of the water molecule.

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