A wire is bet in the form of semi circular ring of radius 0.9m and current 1amp and magnetic induction is n×10^-7tesla find value of n?

Question

I need the answer immediately pls urgent

Answer 1

Hi Nitu:

 

   Since you are quoting a result in units of tesla, I am thinking you are trying to solve for the magnetic field generated by the current.  Often, a problem like this requires you to find the magnetic field at a given position that is relatively easy to calculate with, or has a standard result already derived from, the Biot-Savart law.  For a lot of the circular arc problems we do, that is at the center of the arc, because symmetry makes the derivation of the expression from the Biot-Savart law work out more nicely than at other points inside the arc or on its axis.

 

   If this is the case, the expression for magnetic field generated by the current at the center of a circular arc is:

 

B = (μ_oiφ)/(4πr)

 

where

 

μ_o = 4π x 10^-7  (T•m²/A)   (the (magnetic) permeability of free space, a universal constant)

i = current (Amps)

φ = angle subtended by the arc (radians)

r = radius of the arc (meters)

 

If I use this with the values given, I do get a number on the order of 10^-7 tesla, and I would be happy to check an answer with you or take any other questions about this or similar topics you may have.  Alao, if I am mistaken about the point of the question, please let me know.

 

In our class, this result is derived in our text, and we just use it.  However, if you need to derive it from the Biot-Savart law, I can help you with that, too.  

Answer 2

dB = (μ₀/4π) (IdL x r_hat) / r²

Origin is at location of IdL.

r is from position of circuit element IdL (i.e. the origin) to the field point, which is the center of the semicircle.

r_hat = r/r

 
I = 1A

dL = R dθ

r = R = 0.9 m

Note that IdL ⊥ r_hat, so |IdL x r_hat| = I dL = I Rdθ

Looking just at magnitude,

dB = (μ₀/4π) IdL / r² = (μ₀/4π) IdL / R²

dB = (μ₀/4π) I Rdθ / R²

dB = [μ₀I / (4πR)] dθ

B = [μ₀I / (4πR)] ∫dθ with integration limits in θ from 0 to π (i.e. half way around a loop)

B = [μ₀I / (4πR)] (π)

B = μ₀I / (4R) = (4π x 10^-7)(1) / [4(0.9)] T = 3.491 x 10^-7 T

Given B = n × 10^-7 T, then

n x 10^-7 = 3.491 x 10^-7

n = 3.491