A thin, semi-infinite wire with a constant linear charge density λ extends from −∞ < x ≤ 0. A point charge q is placed at a position x = a with a > 0. Find an expression for the magnitude of the force on q from the wire.

The figure shows a configuration of putual charges that has the value of q1=-2e, q2=2e, q3=4e, q4=e, where e is the fundamental charge. The angle that the charge q1 makes with the negative x axis is θ1= 35.0o. Determine: a) The magnitude of the net force on the charge at the origin b) The angle of the net force on charge four

A positively charged particle Q1 = +25 nC is held fixed at the origin. A second charge Q2 of mass m = 9.5 μg is floating a distance d = 45 cm above charge Q1. The net force on Q2 is equal to zero. You may assume this system is close to the surface of the Earth.  Calculate the magnitude of Q2 in units of nanocoulombs.

a) A charge 4Q is located at x = −2l on the x-axis, and a charge Q is located at x = l on the x-axis. Q > 0. Near the origin, a positive test charge q with mass m undergoes small oscillations along the x-axis. What is the frequency ω of these oscillations? (Remember that if F = ma = −kx, then ω2 = k/m).

Two red blood cells each have a mass of 9.05 × 10-14 kg and carry a negative charge spread uniformly over their surfaces. The repulsion arising from the excess charge prevents the cells from clumping together. One cell carries -3.00 pC and the other -2.60 pC, and each cell can be modeled as a sphere 3.75 × 10-º m in radius. If the red blood cells start very far apart and move directly toward each other with the same speed, what initial speed would each need so that they get close enough to just barely touch? Assume that there is no viscous drag from any of the surrounding liquid. initial speed: m/s What is the maximum acceleration of the cells as they move toward each other and just barely touch? maximum acceleration: m/s?

A ring of radius R that lies in the xy plane carries a positive charge Q uniformly distributed over its lerigth. A particle of mass m that carries a negative charge of magnitude q is at the center of the ring. (a) Show that if x << R, the electric field along the axis of the ring is proportional to z. (b) Find the force on the particle of mass m as a function of z. (c) Show that if m is given a small displacement in the x direction, it will perform simple harmonic motion. Calculate the period of that motion