5.5 Calculating electric fields of charge distributions  (Page 6/12)

Two thin parallel conducting plates are placed 2.0 cm apart. Each plate is 2.0 cm on a side; one plate carries a net charge of $8.0\mu \text{C},$ and the other plate carries a net charge of $\mathrm{-8.0}\mu \text{C}.$ What is the charge density on the inside surface of each plate? What is the electric field between the plates?

A thin conducing plate 2.0 m on a side is given a total charge of $\mathrm{-10.0}\mu \text{C}$ . (a) What is the electric field $1.0\text{cm}$ above the plate? (b) What is the force on an electron at this point? (c) Repeat these calculations for a point 2.0 cm above the plate. (d) When the electron moves from 1.0 to 2,0 cm above the plate, how much work is done on it by the electric field?

A total charge q is distributed uniformly along a thin, straight rod of length L (see below). What is the electric field at $P_1?\text{At}{P}_2?$

Charge is distributed along the entire x -axis with uniform density $\lambda .$ How much work does the electric field of this charge distribution do on an electron that moves along the y -axis from $y=a\text{to}y=b?$

Charge is distributed along the entire x -axis with uniform density ${\lambda }_x$ and along the entire y -axis with uniform density ${\lambda }_y.$ Calculate the resulting electric field at (a) $\overrightarrow{\text{r}}=a\widehat{\text{i}}+b\widehat{\text{j}}$ and (b) $\overrightarrow{\text{r}}=c\widehat{\text{k}}.$

A rod bent into the arc of a circle subtends an angle $2\theta$ at the center P of the circle (see below). If the rod is charged uniformly with a total charge Q , what is the electric field at P ?

A proton moves in the electric field $\overrightarrow{\text{E}}=200\widehat{\text{i}}\text{N/C}.$ (a) What are the force on and the acceleration of the proton? (b) Do the same calculation for an electron moving in this field.

An electron and a proton, each starting from rest, are accelerated by the same uniform electric field of 200 N/C. Determine the distance and time for each particle to acquire a kinetic energy of $3.2\times {10}^{\mathrm{-16}}\text{J}.$

A spherical water droplet of radius $25\mu \text{m}$ carries an excess 250 electrons. What vertical electric field is needed to balance the gravitational force on the droplet at the surface of the earth?

A proton enters the uniform electric field produced by the two charged plates shown below. The magnitude of the electric field is $4.0\times {10}^5\text{N/C},$ and the speed of the proton when it enters is $1.5\times {10}^7\text{m/s}.$ What distance d has the proton been deflected downward when it leaves the plates?

Shown below is a small sphere of mass 0.25 g that carries a charge of $9.0\times {10}^{\mathrm{-10}}\text{C}.$ The sphere is attached to one end of a very thin silk string 5.0 cm long. The other end of the string is attached to a large vertical conducting plate that has a charge density of $30\times {10}^{\mathrm{-6}}{\text{C/m}}^2.$ What is the angle that the string makes with the vertical?

Two infinite rods, each carrying a uniform charge density $\lambda ,$ are parallel to one another and perpendicular to the plane of the page. (See below.) What is the electrical field at $P_1?\text{At}{P}_2?$

Positive charge is distributed with a uniform density $\lambda$ along the positive x -axis from $r\text{to}\infty ,$ along the positive y -axis from $r\text{to}\infty ,$ and along a $90\text{°}$ arc of a circle of radius r , as shown below. What is the electric field at O ?

From a distance of 10 cm, a proton is projected with a speed of $v=4.0\times {10}^6\text{m/s}$ directly at a large, positively charged plate whose charge density is $\sigma =2.0\times {10}^{\mathrm{-5}}{\text{C/m}}^2.$ (See below.) (a) Does the proton reach the plate? (b) If not, how far from the plate does it turn around?

A particle of mass m and charge $\text{−}q$ moves along a straight line away from a fixed particle of charge Q . When the distance between the two particles is $r_0,\text{−}q$ is moving with a speed $v_0.$ (a) Use the work-energy theorem to calculate the maximum separation of the charges. (b) What do you have to assume about $v_0$ to make this calculation? (c) What is the minimum value of $v_0$ such that $\text{−}q$ escapes from Q ?