Magnetic force with spring and resistor problem

In summary, the conversation discusses a problem involving a suspended wire and two springs in a closed circuit. The springs stretch a certain distance when a magnetic field is turned on, and the goal is to find the strength of the magnetic field. The correct method involves finding the spring constant and using it in an equation to solve for the magnetic force. However, the conversation also mentions the importance of converting units and including units in calculations to avoid errors.
  • #1
floridianfisher
27
0
I am having a great deal of trouble solving the following problem. Can anyone help?
A straight wire of mass 10.2 g and length 5.0 cm is suspended from two identical springs that, in turn, form a closed circuit (Fig. P19.66). The springs stretch a distance of 0.51 cm under the weight of the wire. The circuit has a total resistance of 11 . When a magnetic field directed out of the page (indicated by the dots in the figure) is turned on, the springs are observed to stretch an additional 0.30 cm. What is the strength of the magnetic field? (The upper portion of the circuit is fixed.)
 
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  • #2
What have you tried so far?
 
  • #3
I have tried to solve by first find the spring constant by 2kx=mg, then by using that spring constant in a new equation and solving for magnetic force by 2kx-mg=BIL but it is not working out for me.
 
  • #4
Well you seem to have the correct method. Just a point on working out the magnetic force. You can say 2kx = BIL if you use 0.3cm for x.

So is there any more information give about the circuit because you're going to need to know what I is?
 
  • #5
I am solving for I by I+V/R = 2.18 A
 
  • #6
You have all the information and the correct equation so now just rearrange for B and plug all the numbers in.
 
  • #7
I get 539.25 T but when I put it in the computer says I am wrong?
 
  • #8
sorry 539.45 T but stilll wrong
 
  • #9
Have you converted the cm to meters before using them?
 
  • #10
yes I have 2kx=mg, k= 9800 then 2kx-((mg)/(IL))=B
or (10.2*9.8)/(2*0.0051)=9800 and ((2*9800*0.0081)-(10.2*9.8))/(2.18*.05)= 539.45
 
  • #11
Or have you converted grams to kilograms?
 
  • #12
OMG! I am an idiot... Thanks for your help
 
  • #13
When solving a problem, one should put units with the numbers, so that one will sure to use the proper system, either MKS or cgs.
 
  • #14
Another bit of advice is if you have the answer to hand and your answer looks the same but is a number of factors out then check your units. Thats where the discrepency usually is.
 

1. What is the relationship between magnetic force, spring constant, and resistance in this problem?

In this problem, the magnetic force is directly proportional to the spring constant and inversely proportional to the resistance. This means that as the spring constant increases, the magnetic force also increases, while as the resistance increases, the magnetic force decreases.

2. How does the spring affect the behavior of the resistor in this problem?

The spring in this problem acts as a restoring force, pulling the resistor back to its equilibrium position. This can affect the behavior of the resistor by either increasing or decreasing the resistance, depending on the direction and magnitude of the magnetic force.

3. Can the magnetic force, spring constant, or resistance be changed in this problem?

Yes, all three of these variables can be changed. The magnetic force can be changed by altering the strength of the magnetic field or the current in the wire. The spring constant can be changed by using a different spring with a different stiffness. The resistance can be changed by using a different material for the resistor or altering its dimensions.

4. How does the magnetic force affect the motion of the resistor?

The magnetic force will cause the resistor to move in the direction of the force. If the force is strong enough, the resistor may move away from its equilibrium position, causing it to oscillate back and forth around that position due to the spring's restoring force.

5. Is this problem applicable to real-world situations?

Yes, this problem has real-world applications in devices such as electric motors and generators. The magnetic force, spring constant, and resistance can all be found in these types of systems and can be used to model and predict their behavior.

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