A proton is fired from very far away directly at a fixed particle with charge q = 1.82 ✕ 10−18 C. If the initial speed of the proton is 3.5 ✕ 105 m/s, what is its distance of closest approach to the fixed particle? The mass of a proton is 1.67 ✕ 10−27 kg.

Along wire of diameter 1 mm is submerged in an oil bath of temperature ∞ 31°c. the wire has an electrical resistance per unit length of 0.01 ω/m. if a current of 103 a flows through the wire and the convection coefficient is 500 w/m2·k, what is the steady-state temperature of the wire? from the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°c of the steady-state value? the properties of the wire are 8000 kg/m3, 500 j/kg·k, and 20 w/m·k.