106-2018192 Practice for Midterm 2

Disclaimer: These are some random questions which does not have anything to do with the exam. I have no idea or any say about exam questions.

Question 1

Bridge

With the circuit parameters as specified and empty initial charge on the capacitor:

a) Determine the initial current through the capacitor in the instant you switch the power supply on.

b) Draw the charging voltage curve through the capacitor, with the time constant and the maximum voltage numerically and clearly indicated.

  Tip: Thévenin equivalent circuit approach greatly simplifies this problem, if you know how. 

Thevenins Theorem Tutorial

Question 2

A superconducting metal has the property that inside the superconductor both ${\vec {B}}$ and ${\vec {E}}$ is zero.

(a) For the ${\vec {E}}$ field, we found that the boundary condition at the interface of the superconductor is that ${\vec {E}}$ must be normal to the surface, or in other words, that the tangential component must be zero. What is the analogous boundary condition for the magnetic field?

Current loop on top of a superconducting plate

A small current loop with its magnetic moment ${\vec {\mu }}$ oriented at an angle $\theta$ from the normal, is located at a distance $d$ from an infinite, superconducting sheet.

(b) Outline in a few sentences a method for finding the magnetic field everywhere, assuming that you already what the field of a magnetic dipole is.

(c) Find the torque ${\vec {\tau }}$ on the dipole as a function of the angle $\theta$

(d) Deduce the equilibrium angles. Which are stable, which unstable?

(e) Find the force, as a function of $\theta$, towards or away from the superconductor.

solutions