GEO 106 Chapter Notes - Chapter 2: Fibronectin

In this problem, you derive the expression for the self-inductanceof a long solenoid
[L = µ0n2pr2script i].
The solenoid has n turns per unit length, length script i, andradius r. Assume that the current flowing in the solenoid isI.

(a) Write an expression for the magnetic field inside the solenoidin terms of n, script i, r, I, and universal constants.
B = _________________

(b) Assume that all of the field lines cut through each turn of thesolenoid. In other words, assume the field is uniform right out tothe ends of the solenoid—a good approximation if the solenoid istightly wound and sufficiently long. Write an expression for themagnetic flux through one turn.
F = ______________

(c) What is the total flux linkage through all turns of thesolenoid? (Give your answer in terms of N, the total number ofturns, instead of n.)
NF = ______________

(d) Use the definition of self-inductance [NF = LI] to find theself-inductance of the solenoid.
L = ___________

Use the worked example above to help you solve this problem. A W =47.4 N (10.7 lb) weight is held in a person's hand with the forearmhorizontal, as shown in the figure. The biceps muscle is attached d= 0.03033 m from the joint, and the weight is l = 0.354 m from thejoint. Find the upward force vector F exerted by the biceps on theforearm (the ulna) and the downward force vector R exerted by thehumerus on the forearm, acting at the joint. Neglect the weight ofthe forearm.
F = N
F = lb

R = N
R = lb

EXERCISE HINTS: THIS IS WHAT I ACTUALLY NEED HELP WITH!
Use the values from PRACTICE IT to help you work this exercise.Suppose you wanted to limit the force acting on your joint to amaximum value of 8.21 102 N.

(a) Under these circumstances, what maximum weight would youattempt to lift?
Fmax = N

(b) What force would your biceps apply while lifting thisweight?
Fbiceps = N

(part 1 of 3)
A rectangular loop of copper wire of re-
sistance R has width a and length b. The
loop is stationary in a constant, uniform mag-
netic field B0, directed into the page as shown
above.

(part 2 of 3) Let :

n = 9 , a= 9 m, b= 7 m, and B0 = 2 T.

1.E = 120 V

2.E = 1134 V

3.E = 2268 V

4.E = 240 V

5.E = 1440 V

6.E = 0 V

(part 3 of 3)

What is the net magnetic force on the loop of wire?

1.F = 70 N

2.F = 12 N

3.F = 0 N

4.F = 14 N

5.F = 40 N

6.F = 22.2222 N