Question

Name 5 A train of mass mtrain runs along a straight track at speed v. What is the angular momentum of the train relative to a point P that is distance D from the track on the right side (with respect the direction of travel of the train) of the track? [10 pts] 6) Four point charges of +Q are arranged at the corners of a square of side L. Consider the midpoint of each of the four midpoints of the square. At each midpoint, find the direction and magnitude of the electric field. [20 pts]

Answer 1

A Angular momentum of train with respect to point p = Iw [I is M.I of train w.r.t point P] = m_train times D^2 times w = m_train times D^2 times v/B [v = wr] = m_train times v times d (6) Consider the electric field at E_1, E_2, E_3 & E_4 at point O (mid point). E_1 & E_2 will be equal nad opposite So they will cancel out each other Resultant of E_3 & E_4 (E_3 = E_4) will work at 0 E_3 = E_r = 1/4 pi E_0 Q/L62 + L^2/4 = 1/4 pi E_0 4 Q/5 L62 E^2 = E^3_4 + E^2_3 + 2 E_4 E_3 cos theta = 2 E^2_3 + 2 E^2_3 cos theta = 2 E^2_3 (1 + cos theta) = 2 E^2_3 + 2 E^2_3 cos theta/2 E = 2 E_3 cos theta/2 = 2 times 1/4 pi E_0 4 Q/5 L^2 times L/squareroot 5/2 L E = 1/4 pi E_0 times 16Q/5 squareroot 5 L^2.