'''Due Friday, March 9, 2018, by 4 pm in the drop box for your tutorial section.'''

'''Answer all three problems. In order to receive full credit, you must show all of your work. Do not forget to write down your name, student ID, tutorial section and your TA's name. '''

1. Consider the circuit shown below, consisting of five resistors and two (ideal) batteries. Find the currents <math display="inline">I_{3}</math> and <math display="inline">I_{4}</math> through the bottom (''R<sub>3</sub>'') and the diagonal (''R<sub>4</sub>'') resistors. Clearly indicate the directions of the currents in your answer.

[[File:media/image1.jpg|274x214px]]

''R<sub>1</sub>=R<sub>5</sub>''=100 Ohm; ''R<sub>2</sub>=R<sub>3</sub>''=200 Ohm, ''R<sub>4</sub>''=300 Ohm, ''E<sub>1</sub>''=5V, ''E<sub>2</sub>''=3V

2. An infinite conducting cylinder of radius ''R'', oriented along the ''z'' axis, has a cylindrical bore of radius ''r'' inside centered a distance ''c'' away from the origin, as indicated on the picture below. A particle of charge ''q'' happens to be at point P (''x=0, y=d'') moving with velocity ''v'' in +''z''-direction when it experiences a force ''F'' in the +''y''-direction due to the magnetic field created by the current in the conductor.

''r=''1 cm, ''R=4r, d=6r, c=r, q=''500 C'', v=''315 m/s'', F=''0.53 N, m<sub>0</sub>=4p x 10<sup>-7</sup> Tm/A

[[File:media/image2.jpg|263x246px]]

<ol style="list-style-type: lower-alpha;">
<li><p>What is the direction of the current?</p></li>
<li><p>What is the direction of the magnetic field at point P?</p></li>
<li><p>Derive the expression (do not substitute the numbers) for the current in terms of ''r, q, v'', and ''F''. Assume the current density to be uniform in the conductor.</p></li>
<li><p>Find the value of the current in Amperes.</p></li></ol>

3. A physics professor is demonstrating the concept of a “magnetic parachute” using the construction shown in the picture below. The poles and the bar are made of a conducting material that has a negligible resistance, and form a closed loop with a constant resistance ''R=''100 Ohm. The distance between the poles is ''d''=2m. The professor starts from a position that is sufficiently high to reach a constant terminal velocity. The room is filled with a uniform magnetic field B pointing out of the page, as shown. Suppose the professor weighs 80 kg. How strong should the magnetic field be in order for the terminal velocity to be within the safe landing range of v<sub>t</sub> &lt; 8m/s?

[[File:media/image3.jpg|245x391px]]