Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Introduction to gauge theory wikipedia , lookup
Potential energy wikipedia , lookup
Magnetic monopole wikipedia , lookup
Lorentz force wikipedia , lookup
Maxwell's equations wikipedia , lookup
Field (physics) wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Nanofluidic circuitry wikipedia , lookup
PHYS 2421 Exam 1 Spring 2010 NAME___________________________________ Problem 1 (10 points). Determine the point where the total electric field is zero P. 21.44 Solution. By symmetry it has to be between the charges, measuring q q2 q1 r1 from the left charge: E k 12 k d r1 2 0 r1 r1 q2 d r1 d q1 / q2 1.2m 0.5 / 0.8 r1 d q1 / q2 r1 q1 / q2 r1 1 q1 / q2 d q1 / q2 r1 0.53m 1 q1 / q2 1 0.5 / 0.8 Problem 2 (10 points). A hollow conducting sphere is charged up until its surface charge density is + 6.37 106 C / m2 . Then a point charge of q 0.5C is introduced at the center of the sphere as shown. A) What is the new charge density on the outside surface of the sphere? B) What is the magnitude of the electric field just outside the sphere? C) What is the electric flux through a spherical surface just inside the inner surface of the sphere? Probl. 22.23 Solution: 2 A) Total charge in hollow sphere is: QTot 4r2 6.37 106 C / m2 4 0.25m 5 10 6 C , since on the inside surface there are q charges, on the outside there will be QOut QTot q , and the new Q q 5C 0.5C charge density will be Out Tot 2 5.73 106 C / m2 2 4r 4 0.25m Q q 5C 0.5C B) Gauss’ law: E Tot 2 6.474 105 N / C 2 12 2 2 40 r 4 8.85 10 C / N m 0.25m QInside q 0.5 C C) The electric flux is E dA 5.65 104 Nm 2 / C 0 0 8.851012 C 2 / N m2 Problem 3 (10 points). The electric field at the surface of a charged, solid copper sphere is 3800 N/C directed towards the center of the sphere. A) What is the potential at a point 0.175 m from the center of the sphere? B) What is the potential at point B 0.1 m from the center of the sphere? P. 23.44 Solution. A) Since the point 0.175 is inside the conducting sphere, its potential is equal to the kQ potential at outside surface of the sphere: V . But since the field at the surface is R kQ E 2 V ER 3800 N / C 0.2m760 V , and it is negative because the R charge on the sphere is negative. B) Since the field in the hole of the sphere is zero (there are no charges inside), the potential inside the hole is the same as the potential inside the conductor, i.e. V 760 V . Problem 4 (10 points). A dipole consisting of two charges of magnitude q 1.6 10 19 C and 220 nm apart is placed between two large sheets with equal and opposite charge densities of 125 C / m 2 . A) What is the maximum potential energy this dipole can have? B) What is the maximum torque the sheets can exert on the dipole and how it should be oriented relative to the sheets to attain this value? Probl. 21.70 Solution. A) U p E pE cos U Max pE qdE when the dipole makes qd an angle of 180o respect to the field. But E / 0 U Max qdE 0 or U Max 1.6 10 19 C 220 10 m 125C / m 4.97 10 9 8.85 10 12 2 C /N m 2 2 19 Nm or Joules. B) p E pE sin 19 9 2 qd 1.6 10 C 220 10 m 125C / m Max pE 4.97 1019 Nm . This happens when 0 8.85 10 12 C 2 / N m2 sin 1 90 , the dipole should be aligned parallel to the sheets, i.e. perpendicular to the electric field. 0