Circular loop of a wire and a long straight wire carry currents $I_c$ and $I_e$, respectively as shown in figure. Assuming that these are placed in the same plane, the magnetic fields will be zero at the centre of the loop when the separation $H$ is
AIIMS 2006, Medium
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Magnetic field due to straight wire $ = \,\frac{{{\mu _0}{I_e}}}{{2\pi H}}$
Magnetic field due to circular wire $ = \,\frac{{{\mu _0}{I_c}}}{{2R}}$
Now $\frac{{{\mu _0}{I_e}}}{{2\pi H}} = \frac{{{\mu _0}{I_c}}}{{2R}}$
$ \Rightarrow \,\,H = \frac{{R{I_e}}}{{\pi {I_c}}}$
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