Coulomb’s law: In the figure, charge q1 =  3.1 × 10-6  C is…

Coulomb’s law: In the figure, charge q1 =  3.1 × 10-6  C is placed at the origin and charge  q2 =  -8.7 × 10-6 C  is placed on the x-axis, at x = -0.20 m. Where along the x-axis can a third charge Q = -8.3 µC be placed such that the resultant force on this third charge is zero? 

Energy in capacitors: An ideal parallel-plate capacitor cons…

Energy in capacitors: An ideal parallel-plate capacitor consists of a set of two parallel plates of area A separated by a very small distance d. When this capacitor is connected to a battery that maintains a constant potential difference between the plates, the energy stored in the capacitor is U0. If the separation between the plates is doubled, how much energy is stored in the capacitor?

Current density: A proton beam that carries a total current…

Current density: A proton beam that carries a total current of 1.3 mA has 10.0 mm diameter. The current density in the proton beam increases linearly with distance from the center. This is expressed mathematically as J(r) = J0 (r/R), where R is the radius of the beam and J0 is the current density at the edge. Determine the value of J0.