Electrical potential in an electric field is given by V = K/r (K being constant). If the position vector F = 2î +3}+6k, then the electric field will be (2î +3 j + 6k) , (2î +3 ĵ + 6k) » (a) K 243 (b) 343 (3i +23 + 6Â) , (6i +2 j + 6k , (c) K (d) -K 243 343

Given that E = (3x2 + y) ax + x ay (kV/m), find the work done in moving a -2µC charge from (0,5,0) to (2,-1,0) by taking path:(a) (0,5,0) → (2,5,0) → (2,-1,0)(b) y = 5 – 3x

A proton is located at the origin, and a second proton is located on the x-axis at x1 = 6.22 fm (1 fm = 10−15 m). (a) Calculate the electric potential energy associated with this configuration. J (b) An alpha particle (charge = 2e, mass = 6.64 ✕ 10−27 kg) is now placed at (x2, y2) = (3.11, 3.11) fm. Calculate the electric potential energy associated with this configuration. J (c) Starting with the three particle system, find the change in electric potential energy if the alpha particle is allowed to escape to infinity while the two protons remain fixed in place. (Throughout, neglect any radiation effects.) J (d) Use conservation of energy to calculate the speed of the alpha particle at infinity. m/s (e) If the two protons are released from rest and the alpha particle remains fixed, calculate the speed of the protons at infinity. m/s

(III) In the Bohr model of the hydrogen atom, an electron orbits a proton (the nucleus) in a circular orbit of radius 0.53 × 10-10 m. (a) What is the electric potential at the electron's orbit due to the proton? (b) What is the kinetic energy of the electron? (c) What is the total energy of the electron in its orbit? (d) What is the ionization energy– that is, the energy required to remove the electron from the atom and take it to r = ∞, at rest? Express the results of parts (b), (c), and (d) in joules and eV.