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TS EAMCET · Physics · Magnetic Effects of Current

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)

  1. A 2
  2. B 1
  3. C 3
  4. D \(\sqrt{5}\)
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Correct Answer

(C) 3

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Detailed explanation

Magnetic field due to axial magnet, \( \mathbf{B}_1=\frac{\mu_0}{4 \pi} \frac{2 M}{d^3} \quad \text { (+Y direction) } \) Magnetic field due to equatorial magnet, \( \mathbf{B}_2=\frac{\mu_0}{4 \pi} \frac{M}{d^3} \quad \text { (+Y direction) } \) So, effective magnetic field…
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