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  • FInd out net magnetic field at point 0 . due to given arrangement . I current is flowing through arrangement (r <img alt="\rightarrow" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Crighta

FInd out net magnetic field at point 0 . due to given arrangement . I current is flowing through arrangement (r \rightarrow radius )

Option: 1

\frac{\mu _0i}{4\pi r}


Option: 2

\frac{\mu _0i}{2 r}


Option: 3

0


Option: 4

\frac{3}{8}\frac{\mu _0i}{ r}


Answers (1)

best_answer

Let the magnetic field due to small and big arcs which are subtending angle \theta and 2\pi-\theta at O be B1 and B2 respectively

B_1= \frac{\mu_0 i_1\theta}{4 \pi r} \ \ \ \text{(Out of the plane)}

B_2= \frac{\mu_0 i_2(2\pi- \theta)}{4 \pi r} \ \ \ \text{(into the of the plane)}

The current through the arc 1 and arc 2 be i1 and i2 respectively

i=i1+i2

\\ i_1R_1=i_2R_2

\because R=\frac{\rho l}{A}

\\ i_1l_1=i_2l_2 \\ i_1(r \theta)=i_2(r (2\pi-\theta)) \\ \Rightarrow i_1\theta=i_2 (2\pi-\theta)

By solving above equations

B_{net}=B_1+B_2=0

 

 

Posted by

Pankaj Sanodiya

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