Two short bar magnets have their magnetic moments $1.2 \mathrm{Am}^2$ and $1.0 \mathrm{Am}^2$. They are…

Two short bar magnets have their magnetic moments $1.2 \mathrm{Am}^2$ and $1.0 \mathrm{Am}^2$. They are placed on a horizontal table parallel to each other at a distance of $20 \mathrm{~cm}$ between their centres, such that their north poles pointing towards geographic south. They have common magnetic equatorial line. Horizontal component of earth's field is $3.6 \times 10^{-5} \mathrm{~T}$. Then, the resultant horizontal magnetic induction at mid point of the line joining their centers is $\left(\frac{\mu_0}{4 \pi}=10^{-7} \mathrm{~N} / \mathrm{m}\right)$
  1. $3.6 \times 10^{-5} \mathrm{~T}$
  2. $1.84 \times 10^{-4} \mathrm{~T}$
  3. $2.56 \times 10^{-4} \mathrm{~T}$
  4. $5.8 \times 10^{-5} \mathrm{~T}$

Solution

We knows, $B=\frac{\mu_0}{4 \pi} \frac{M}{r^3}$ Hence the resultant horizontal magnetic induction point of the line joining their conters is $\begin{aligned} B & =B_1+B_2+B_H \\ & =\frac{10^{-7} \times 1.2}{\left(10 \times 10^{-2}\right)^3}+\frac{10^{-7} \times 1}{\left(10 \times 10^{-2}\right)^3}+3.6 \times 10^{-5} \\ & =1.2 \times 10^{-4}+1 \times 10^{-4}+0.36 \times 10^{-4} \\ & =2.56 \times 10^{-4} \mathrm{~T} \end{aligned}$

Asked in: AP EAMCET 2013

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