Magnetic Effects & Magnetism

JEE Main level, single correct, medium

268 of 276

Question 268 of 276

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1{B}_{1} . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is B2{B}_{2} . The ratio B1B2\dfrac{{B}_{1}}{{B}_{2}} is:

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Answer: (D) 2\sqrt{2}

m=m=magnetic dipole moment=IA=IA. For Loop1Loo{p}_{1}, m=Iπr2m=I\pi {r}^{2}, B1=μ0i2r{B}_{1}=\dfrac{{\mu }_{0}i}{2r}
For Loop2Loo{p}_{2}. If current is constant m is doubled. r1=2r{r}^{1}=\sqrt{2}r. B2=μ0i22r{B}_{2}=\dfrac{{\mu }_{0}i}{2\sqrt{2}r}.B1B2=2\dfrac{{B}_{1}}{{B}_{2}}=\sqrt{2}

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