MHT CET · Physics · Magnetic Effects of Current
Two short bar magnets 'A and 'B' (having magnetic moments ' \(\mathrm{M}_{1}\) ' and ' \(\mathrm{M}_{2}\) '
respectively) are kept one above the other with their magnetic axis perpendicular
to each other. If their resultant at a point on the axis of magnet ' \(A\) ' is inclined at \(45^{\circ}\) with the axis of magnet A then the ratio of magnetic moments \(\frac{\mathrm{M}_{2}}{\mathrm{M}_{1}}\) is \(\left[\tan 45^{\circ}=1\right]\)
- A \(2: 1\)
- B \(2: 3\)
- C \(1: 2\)
- D \(3: 2\)
Answer & Solution
Correct Answer
(A) \(2: 1\)
Step-by-step Solution
Detailed explanation
\(B_{1}=\frac{2 \mu_{0} M_{1}}{4 \pi d^{3}} \quad B_{2}=\frac{-\mu_{0} M_{2}}{4 \pi d^{3}}\)
\(\tan 45=\left|\frac{B_{2}}{B_{1}}\right|\)
\(1=\frac{M_{2}}{2 M_{1}} \Rightarrow \quad M_{2}: N+2: 1\)
\(\Rightarrow M_{2}: M_{1}=2: 1\)
\(\tan 45=\left|\frac{B_{2}}{B_{1}}\right|\)
\(1=\frac{M_{2}}{2 M_{1}} \Rightarrow \quad M_{2}: N+2: 1\)
\(\Rightarrow M_{2}: M_{1}=2: 1\)
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