DAY 12 -- Homework

1. A square loop of wire that measures 10 cm on a side carries a current of 2 A. The plane of the loop makes a 45^o angle with a uniform B field of strength 0.5 T. Find the torque on the loop. Find the maximum torque that the field can apply to the loop.

2. Use Ampere’s Law to derive the equation for the magnetic field of a solenoid.

HINT – You can probably find this done in many physics books.


B-field Program – CLICK HERE

Use the B-field demo program (see overview section for a slightly different version) to answer the next three questions. Note that if you click and hold down the mouse button the program will read the B-field strength.

3. Create a 5-loop solenoid. What is the field strength in the solenoid? Add five more loops and repeat. Continue the process until you have created a solenoid long enough that the field strength outside the solenoid is less than 5% the strength inside. Note that the solenoid will extend off the screen -- that is OK. Discuss what happens to the strength of the field as the solenoid gets longer? Make a chart to illustrate your answer. Does the field inside the solenoid get more uniform as the solenoid gets longer? Explain? What happens to the divergence of the field lines at the ends of the solenoid as it gets longer?

4. In the above problem, as the solenoid gets longer, do you think the strength of the N & S poles of the solenoid gets weaker (in terms of their ability to attract ferrous materials)? Stronger? Weaker then stronger? Stronger then weaker? Explain.

5. Based on the field in your longest solenoid, determine the current flowing through the coil.

6. Use this program (click here) and the B-field program from above. Consider the following configurations of wires:
i -- one wire carrying current.
ii -- two wires carrying identical current in opposite directions.
iii -- a hollow tube carrying current.
iv -- a coaxial cable carrying identical current in opposite directions.
v -- one wire carrying no current.

(a) Which of these will look the same from a distance, magnetically speaking?
(b) Which of these will look the same when nearby?
(c) Using Ampere's Law, explain the hollow tube's magnetic field.
(d) Using Ampere's Law, explain the coaxial cable's magnetic field.

7. In the figure below determine how the current loop will move if it is free to do so.

8. In the figure below, determine how the current loop will move if it is free to do so. What if the loop were at A? B? C?

9. In the figure below, how will the small loop on the left side of the solenoid move? How will the small loop on the right side move? How will the loop on the right side move if it were located at A? B?

10.PHY 232 ONLY. A loop of current (I = 2 A, diameter 2 mm), sits in a non-uniform B-field, flow clockwise as see in the picture below. The field is radially symmetric, and the loop is centered on the axis of symmetry. If, at the loop’s location, the B-field has magnitude 2T and makes a 35^o angle with the vertical, calculate the force on the loop. Is it attractive or repulsive?

11.What strength magnetic field would be needed if the motor in today’s Example #1 was to generate 0.75 Hp (all other factors remain the same)?