A small rod of length 1.0 cm is placed along the x-axis and has a linear charge density given by λ=αx, where α=3.0 C/cm^2 and x is measured from the center of the rod.

The surface charge density (eta) h of an infinite charged plane is -2.0 x 10-6 C/m2. A proton is shot straight away from the plane at 2.0 x 106 m/s. Make a sketch of the situation. How far does the proton travel before reaching its turning point?

An infinite line of positive charge lies along the y axis, with charge density A = 1.10 µC/m. A dipole is placed with its center along the x axis at x = 21.0 cm. The dipole consists of two charges ±10.0 µuC separated by 2.00 cm. The axis of the dipole makes an angle of 25.0° with the x axis, and the positive charge is farther from the line of charge than the negative charge. Find the net force exerted on the dipole.

2 narrow, flat metal plates are positioned vertically, 20.00 cm. The first plate has a positive charge with charge density σ=+630.0 mC/m2 and a second plate has an equal but opposite negative charge with charge density σ=-6300.0 mC/m2 . There are also two narrow, flat metal plates positioned horizontally, 30.00 cm apart, with the top plate given a negative charge, and the bottom plate given an equal but opposite positive charge, such that the electric potential of the bottom plate is 5.00 V higher than the top plate. A small sphere with a mass of m =64.35 g, and a charge of q =22.00 mC is attached to a narrow, stiff, massless, insulating rod with a length of L= 8.00 cm, which is pivoted at point O, which is 2.000 cm from the second plate. The sphere/rod unit is angled at 5 degrees with horizontal and released from rest. Will the sphere/rod ever hit an angle of 0 degrees with the horizontal? If so, how long will it take to reach that point?

Two identical conducting spheres each having a radius of 0.500 cm are connected by a light 2.20 m long conducting wire. A charge of 56.0 µC is placed on one of the conductors. Assume the surface distribution of charge on each sphere is uniform. Determine the tension in the wire.

Spherical shell of inner radius R₁ = 1.3R and outer radius R₂ = 4.15R is filled uniformly with charge density p. A point charge Q = 4.8q is located at point A a distance 7.99 R from the center of the sphere. What is the magnitude of the force acts on the sphere by the point charge. Express your answer in terms of qpR/ using two decimal places. R2 Answer: R₁ P A Q

Problem 4: Charge Q1 = 2.8 µC is located at r = (3.4i – 2.0j + 4.5k) m. A second charge Q, = 3.9 µC is located at r, = (8.0i – 3.6j – 9.0k) m. Part (a) What is the magnitude of the force of the second charge on the first charge in newtons? Numeric :A numeric value is expected and not an expression. Part (b) The force of the second charge on the first charge can be written using unit vectors as follows: F= Fi+F,j+F,k What is the value of F, in newtons? Numeric :A numeric value is expected and not an expression. Part (c) What is the value of F, in newtons? Numeric :A numeric value is expected and not an expression. Fy- Part (d) What is the value of F, in newtons? Numeric :A numeric value is expected and not an expression.

A hydrogen atom is made up of a proton of charge +Q = 1.6x10-19C and an eledron of charge -Q = 1.6x10-19C. The proton may be regarded as a point charge at r = 0 the center of the atom. The motion of the eledtron causes its charge to be "smeared ouť into a spherical distribution around the proton, so that the electron is equivalentto a charge per unitvolume of (7) =-(Q/ra?)e"lao, where a, = 5.29x10-11 m is called the Bohr radius. (a) Find the total amount of the hydrogen atom's charge that is endosed within a sphere with radius centered on the proton. (b) Find the eledricfield (magnitude and diredion) caused by the charge of the hydrogen atom as a fundtion of (c) Make a graph as a function of rof the ratio of the eledtricfield magnitude to the magnitude of the field due to the proton alone Set up: 1. 1. The charge distribution in this task is spherically symmetric, so you can solve it using Gauss's law. 2. The charge within a sphere of radius r indudes the proton charge Qplus the…

A conducting sphere of radius r1 = 0.46 m has a total charge of Q = 2.9 μC. A second uncharged conducting sphere of radius r2 = 0.23 m is then connected to the first by a thin conducting wire. The spheres are separated by a very large distance compared to their size. r1 = 0.46 mr2 = 0.23 mQ = 2.9 μC What is the total charge on sphere two, Q2 in coulombs?

Four solid plastic cylinders all have radius 2.55 cm and length 6.48 cm. Find the charge of each cylinder given the following additional information about each one. Cylinder (a) carries charge with uniform density 15.8 nC/m² everywhere on its surface. Cylinder (b) carries charge with uniform density 15.8 nC/m² on its curved lateral surface only. Cylinder (c) carries charge with uniform density 525 nC/m3 throughout the plastic. Cylinder (d) carries charge with uniform linear density 54.2 nC/m along the length of the plastic.