Please help me simplify this equation >_<

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In summary, the conversation is about finding the magnetic field at the center of a solenoid using the equation B = uNI/2L. The person is asked to calculate the difference in the field between a finite length solenoid and an infinitely long solenoid. They provide their values for L, R, and I and get a result of 520%, but are unsure if it is correct due to a possible missing parenthesis in the equation.
  • #1
vaxopy
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[tex]B = uNI/2L * (L/2/(\sqrt{((L/2)^2)+R^2)} - (-L/2/(\sqrt{((-L/2))^2+R^2))}[/tex]

I get.. [tex]B = uNI/2R[/tex] (for those wondering, this is the equation to find the magnetic field when a Hall probe is placed in the center of a solenoid)

they ask me to figure out the % diffeerence between the field at the center of the solenoid compared to a solenoid that infinitely long (where B = uNI)..

I get L = 28cm, R = 2.69cm, I = 1.25A

i get 520% when using my simplified formula >_<
is this right?

and i don't even use the current!
 
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  • #2
It's hard to tell- you are clearly missing at least one parenthesis. Is the initial
(uNI/2L) multiplied by BOTH fractions (in which case they clearly add) or is it multiplying only the first fraction (which is what you have written- and is much harder).
 
  • #3


Sure, I'd be happy to help simplify this equation for you! First, let's break down the given equation into smaller parts:

- u: This represents the permeability of the medium, which is a constant value.
- N: This represents the number of turns in the solenoid coil.
- I: This represents the current flowing through the solenoid.
- L: This represents the length of the solenoid.
- R: This represents the radius of the solenoid.

Now, let's take a closer look at the first part of the equation: uNI/2L. We can simplify this by dividing both the numerator and denominator by 2, giving us uNI/L. This is because dividing by 2 in both the numerator and denominator is the same as dividing by 2L.

Next, let's look at the second part of the equation: (L/2/(\sqrt{((L/2)^2)+R^2)} - (-L/2/(\sqrt{((-L/2))^2+R^2)). This part can be simplified by first rewriting it as (L/2)/\sqrt{((L/2)^2)+R^2} - (-L/2)/\sqrt{((-L/2))^2+R^2}. This is because the division sign can be rewritten as a fraction. Next, we can simplify the fractions by multiplying both the numerator and denominator by 2, giving us L/\sqrt{(L^2)+4R^2} - (-L/\sqrt{(L^2)+4R^2}. Simplifying further, we get L/\sqrt{(L^2)+4R^2} + L/\sqrt{(L^2)+4R^2}. Finally, we can combine these two terms by adding them together, giving us 2L/\sqrt{(L^2)+4R^2}.

Now, let's put everything back together: B = uNI/L * 2L/\sqrt{(L^2)+4R^2}. We can further simplify this by canceling out the Ls, leaving us with B = uNI/\sqrt{(L^2)+4R^2}. This is the simplified form of the original equation.

To answer the question about the difference between the magnetic field at the center of a finite solenoid compared to an infinitely long solenoid, we can use this simplified
 

1. What does it mean to "simplify" an equation?

Simplifying an equation means to manipulate it algebraically to make it easier to understand or solve. This can involve combining like terms, factoring, or using other techniques to make the equation more concise.

2. How do I know if an equation can be simplified?

Most equations can be simplified in some way. Look for terms that can be combined or factors that can be pulled out. If an equation has variables on both sides, it can often be rearranged to make it simpler.

3. Can I simplify an equation without changing its meaning or solution?

Yes, simplifying an equation should not change its meaning or solution. As long as you are following the rules of algebra, you can manipulate the equation in any way that makes it clearer or easier to solve.

4. What are some common techniques for simplifying equations?

Some common techniques include combining like terms, factoring, using the distributive property, and simplifying fractions. It is also helpful to follow the order of operations and work from the inside out when simplifying complex equations.

5. How can I check if my simplified equation is correct?

You can check your simplified equation by substituting the values of the variables into both the original and simplified equations and comparing the results. You can also use a graphing calculator to graph both equations and see if they produce the same graph.

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