Two large, parallel conducting plates carrying op­posite charges of equal magnitude are separated by $2.20$ cm. If the surface charge density for each plate has magnitude $47.0$ nC/m², what is the magnitude of $E$ in the region between the plates?

A very long insulating cylinder of charge of radius $2.50$ cm carries a uniform linear density of $15.0$ nC/m. If you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads $175$ V?

An infinitely long line of charge has linear charge den­sity $5.00\times {10}^{-12}$ C/m. A proton (mass $1.67\times {10}^{-27}$ kg, charge $+1.60\times {10}^{-19}$ C) is $18.0$ cm from the line and moving directly toward the line at $3.50\times {10}^3$ m/s. Calculate the proton's initial kinetic energy.

Certain sharks can detect an electric field as weak as $1.0$ $\mu$V/m. To grasp how weak this field is, if you wanted to produce it between two parallel metal plates by connecting an ordinary $1.5$­V AA battery across these plates, how far apart would the plates have to be?

Two large, parallel conducting plates carrying op­posite charges of equal magnitude are separated by $2.20$ cm. What is the potential difference between the two plates?

Two large, parallel conducting plates carrying op­posite charges of equal magnitude are separated by $2.20$ cm. The surface charge density for each plate has magnitude $47.0$ nC/m^2. If the separation between the plates is doubled while the surface charge density is kept constant at the given value, what happens to the magnitude of the electric field and to the po­tential difference?

An infinitely long line of charge has linear charge den­sity $5.00\(\times\)10^{-12}$ C/m. A proton (mass $1.67\(\times\)10^{-27}$ kg, charge $+1.60\(\times\)10^{-19}$ C) is $18.0$ cm from the line and moving directly toward the line at $3.50\(\times\)10^3$ m/s. How close does the proton get to the line of charge?