PHYS 211 Exam 2, Fall 2005

Physics 211 Quiz 2 Ap7.il25, 2005 Your name: ID number: Time given: 60 minutes Please provide your reasoning for each step of your solution (providixig an answer without a solution is not enough) www.amal-aub.org Problem 1 ( 4 0 f t 5 ) A spherical conducting shell with the internal and the external radii equal to Rl and R.z has a non-constant resistivity which grows line* with the distance r from the origin 0: p(r) = ar (R1 _< r 5 Rz) where a is a. given constant. a)Find the t,otal resistance between the inner and the outer surfaces of the shell b)Find the current density i ( r ) as a function of r if a potential difference between the inner and the outer surfaces is equal to AV Q-- www.amal-aub.org Problem 2 ( 0 P 1 In the circuit shown on t.he Figure 1, the resistances are R1 = 1R: = 2St, I23 = 4SZ and the voltages of the batteries AVl = 2V, AV2 = 3V, AV3 = 5V. The capacitance C of the capacitor is unknown. The switches A and B are turned on simultaneously at t = 0. a)Find the currents 11, Iz, I3 through the resistors R1, R2, R.3 at t = 0, i.e. inmediately r-- - after the switches are closed. b)Find the currents 11: 12, I3 through all of the resistors at t = m, i.e. after the switches would have been closed for a. veqr long (infinite) time. www.amal-aub.org Problem 3 (2 0 P &S ) A non-uniform magnetic field has the form: B(z, y, z) = yzz+ 2%~; + 3 r y i (T) At a certain moment a charged particle moving with the velocity v' = 5+ j + (:)is passing through the point A with the coordinates 107f y.T + zc(rn) where the values of y and z are unknown. Find the coordinates of the point A if it is known that the force exerted on the particle by the magnetic field is zero at the moment, the particle is passing the point A. www.amal-aub.org