A solid conducting sphere of radius 3.0 cm has a charge of 30 nC distributed uniformly over its surface. Let A be a point 1.0 cm from the center of the sphere, S be a point on the surface of the sphere, and B be a point 5.0 cm from the center of the sphere. What are the electric potential differences $V_A - V_B$?

It is postulated that the radial electric field of a group of charges falls off as $E_r=C l r^n$, where $C$ is a constant, $r$ is the distance from the center of the group, and $n$ is an unknown exponent. To test this hypothesis, you make a field probe consisting of two needle tips spaced $1.00 \mathrm{~mm}$ apart. You orient the needles so that a line between the tips points to the center of the charges. then use a voltmeter to read the potential difference between the tips. After you take measurements at several distances from the center of the group, your data are as follows:

Use an appropriate graph of the data to determine the constants $C$ and $n$.

Two large, parallel, conducting plates are $12 \mathrm{~cm}$ apart and have charges of equal magnitude and opposite sign on their facing surfaces. An electrostatic force of $3.3 \times 10^{-15} \mathrm{~N}$ acts on an electron placed anywhere between the two plates. (Neglect fringing.) (a) Determine the electric field at the position of the electron. (b) What is the potential difference between the plates?

The solid metal sphere of radius $a=0.200 \mathrm{~m}$ shown in the figure has a surface charge distribution of $\sigma$. The potential difference between the surface of the sphere and a point $P$ at a distance $r_{\mathrm{p}}=0.500 \mathrm{~m}$ from the center of the sphere is $\Delta V=V_{\text {surface }}-V_{\mathrm{p}}=+4 \pi \mathrm{V}=+12.566 \mathrm{~V}$. Determine the value of $\sigma$.

On planet Tehar, the free-fall acceleration is the same as that on the Earth, but there is also a strong downward electric field that is uniform close to the planet’s surface. A 2.00-kg ball having a charge of 5.00 $\mu C$ is thrown upward at a speed of 20.1 m/s. It hits the ground after an interval of 4.10 s. What is the potential difference between the starting point and the top point of the trajectory?

A delivery truck with 2.8-m-high aluminum sides is driving west at 75 km/h in a region where the earth's magnetic field is $\vec { B } = \left( 5.0 \times 10 ^ { - 5 } \mathrm { T } , \text { north } \right)$. a. What is the potential difference between the top and the bottom of the truck's side panels? b. Will the tops of the panels be positive or negative relative to the bottoms?

A metal strip $6.5 \mathrm{~cm}$ long, $0.88 \mathrm{~cm}$ wide, and $0.76 \mathrm{~mm}$ thick moves with constant speed $v$ through a magnetic field $B=$ $1.2 \mathrm{mT}$ perpendicular to the strip, as shown in Figure.1 potential difference of $3.9 \mu \mathrm{V}$ is measured between points $x$ and $y$ across the strip. Calculate the speed $v$.

How much energy is stored by an electric eel when it has the potential difference of 650 V? Use the parallel-plate model discussed in Problem 120. A. $1.8 \times 10^{-17} \mathrm{J}$ B. $1.7 \times 10^{-8} \mathrm{J}$ C. $1.6 \times 10^{-6} \mathrm{J}$ D. $2.0 \times 10^{-2} \mathrm{J}$

(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength of dry air, which is $3.00 \times 10 ^ { 6 } \mathrm { V } / \mathrm { m }$, if the plates are separated by 2.00 mm mm and a potential difference of $5.0 \times 10 ^ { 3 } \mathrm { V }$ is applied? (b) How close together can the plates be with this applied voltage?

A manufacturer claims that a carpet will not generate more than $5.0 \mathrm{kV}$ of static electricity. What magnitude of charge would have to be transferred between a carpet and a shoe for there to be a $5.0-\mathrm{kV}$ potential difference between the shoe and the carpet. Approximate the shoe and the carpet as large sheets of charge separated by a distance $d=1.0 \mathrm{~mm}$.

Express in eV (or keV or MeV if more appropriate): a. The kinetic energy of a $\mathrm{Li}^{++}$ion that has accelerated from rest through a potential difference of $5000 \mathrm{~V}$. b. The potential energy of two protons $10 \mathrm{fm}$ apart. c. The kinetic energy, just before impact, of a $200 \mathrm{~g}$ ball dropped from a height of $1.0 \mathrm{~m}$.

The work done by an external force to move a $-8.50 \mu \mathrm{C}$ charge from point a to point b is $15.0 \times 10^{-4} \mathrm{J}$ If the charge was started from rest and had $4.82 \times 10^{-4} \mathrm{J}$ of kinetic energy when it reached point b, what must be the potential difference between a and b?

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has a radius $12.5 \textrm{ cm}$, and the outer sphere has a radius $14.8 \textrm{ cm}$. A potential difference of $120 \textrm{ V}$ is applied to the capacitor.

What is the energy density at $r = 14.7 \textrm{ cm}$, just inside the outer sphere?

A resistor is constructed by forming a material of resistivity $3.5 \times 10 ^ { 5 } \Omega \cdot \mathrm { m }$ into the shape of a hollow cylinder of length 4.0 cm and inner and outer radii 0.50 cm and 1.2 cm, respectively. In use, a potential difference is applied between the ends of the cylinder, producing a current parallel to the length of the cylinder. Find the resistance of the cylinder.