Two short bar magnets each of magnetic moment of $9 \mathrm{Am}^2$ are placed such that one is at $x=-3 \mathrm{~cm}$ and the other at $y=-3 \mathrm{~cm}$. If their magnetic moments are directed along positive and negative $X$-directions respectively, then the resultant magnetic field at the…

Question

Two short bar magnets each of magnetic moment of $9 \mathrm{Am}^2$ are placed such that one is at $x=-3 \mathrm{~cm}$ and the other at $y=-3 \mathrm{~cm}$. If their magnetic moments are directed along positive and negative $X$-directions respectively, then the resultant magnetic field at the origin is

Aicharya · Accepted Answer

At origin, both magnetic fields will be in same direction.

Magnetic field due to $M_1$ (axial point) $ \begin{aligned} & B_1=\frac{\mu_0}{4 \pi} \times \frac{2 M}{r^3}=10^{-7} \times \frac{2 \times 9}{27 \times 10^{-6}} \\ & B_1=\frac{2}{3} \times 10^{-1} \mathrm{~T} \end{aligned} $ Magnetic field due to $M_2$ (equatorial point) $ B_2=\frac{\mu_0}{4 \pi} \times \frac{M}{r^3}=10^{-7} \times \frac{9}{27 \times 10^{-6}}=\frac{1}{3} \times 10^{-1} \mathrm{~T} $ As both $B_1$ and $B_2$ points in same direction, so effective field, $B=\left(\frac{1}{3}+\frac{2}{3}\right) \times 10^{-1} \mathrm{~T}$ $ \Rightarrow \quad B=10^{-1} \mathrm{~T}=0.1 \mathrm{~T} $

Two short bar magnets each of magnetic moment of $9 \mathrm{Am}^2$ are placed such that one is at $x=-3…

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