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Two long parallel wires 1 and 2 separated by a distance d carry equal currents I as shown in Fig. The magnetic field at the point p which is exactly mid-way between the two wires is.

Option: 1

\mathrm{\frac{2 \mu_0 I}{\pi d} ~into ~the ~page}


Option: 2

\mathrm{\frac{\mu_0 I}{\pi d} ~out ~of ~the ~page}


Option: 3

\mathrm{\frac{\mu_0 I}{2 \pi d} ~into ~the ~page}


Option: 4

\mathrm{zero}


Answers (1)

best_answer

The magnitude of the magnetic field at a point at a distance r from a long wire carrying a current I is given by:
\mathrm{B=\frac{\mu_0 I}{2 \pi r} }


Therefore, the magnitude of the magnetic field at point P due to current in wire 1 is (since \mathrm{r = d / 2 } ).
\mathrm{ B_1=\frac{\mu_0 I}{2 \pi(d / 2)}=\frac{\mu_0 I}{\pi d} }


From the right- hand thumb rule, the direction of the field is into the page. For wire 2,
\mathrm{ B_2=\frac{\mu_0 I}{\pi d} \quad \text { out of the page } }


These two fields have equal magnitude but opposite direction. Hence they cancel each other. So the correct choice (4).

Posted by

seema garhwal

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