Q. No.
A square loop with a side \(l\) is held in a uniform magnetic field \(B\), such that its plane making an angle \(\alpha\) with \(B\). A current \(i\) flows through the loop. What will be the torque experienced by the loop in this position?
1. \(Bil^{2}\)
2. \(Bil^{2} \sinα\)
3. \(Bil^{2} \cosα\)
4. zero
1. \(Bil^{2}\)
A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is \(60^{\circ}\), and one of the fields has a magnitude of \(1.2\times 10^{-2}~\text{T}\). If the dipole comes to stable equilibrium at an angle of \(15^{\circ}\) with this field, what is the magnitude of the other field? \(\left[\text{Given} : \sin 15^ \circ = 0 . 26\right]\)
1. \( 7.29 \times10^{-3} ~\text{T} \)
2. \( 4.39 \times10^{-3} ~\text{T} \)
3. \( 6.18 \times10^{-3} ~\text{T} \)
4. \(5.37 \times10^{-3} ~\text{T} \)
| (a) | \(\oint B\cdot dl= \mp 2\mu_0 I\) |
| (b) | the value of \(\oint B\cdot dl\) is independent of the sense of \(C\). |
| (c) | there may be a point on \(C\) where \(B\) and \(dl\) are perpendicular. |
| (d) | \(B\) vanishes everywhere on \(C\). |
Which of the above statements is correct?
| 1. | (a) and (b) | 2. | (a) and (c) |
| 3. | (b) and (c) | 4. | (c) and (d) |
| 1. | \( \dfrac{{IL}^2}{4} ~\text{A}\text-\text{m}^2 \) | 2. | \( \dfrac{{I} \times \pi {L}^2}{4} ~\text{A}\text-\text{m}^2 \) |
| 3. | \( \dfrac{2 {IL}^2}{\pi}~\text{A}\text-\text{m}^2 \) | 4. | \( \dfrac{{IL}^2}{4 \pi}~\text{A}\text-\text{m}^2 \) |
| 1. | resistance of \(19.92~ \text{k} \Omega\) parallel to the galvanometer |
| 2. | resistance of \(19.92~ \text{k} \Omega\) in series with the galvanometer |
| 3. | resistance of \(20 ~\Omega\) parallel to the galvanometer |
| 4. | resistance of \(20~ \Omega\) in series with the galvanometer |
| 1. | \({G \over (S+G)}\) | 2. | \({S^2 \over (S+G)}\) |
| 3. | \({SG \over (S+G)}\) | 4. | \({G^2 \over (S+G)}\) |
1. \(1.5\times10^{-3}\) Nm
2. \(1.5\times10^{-2}\) Nm
3. \(3\times10^{-2}\) Nm
4. \(3\times10^{-3}\) Nm
The resistances of three parts of a circular loop are as shown in the figure. What will be the magnetic field at the centre of \(O\)
(current enters at \(A\) and leaves at \(B\) and \(C\) as shown)?
| 1. | \(\dfrac{\mu_{0} I}{6 a}\) | 2. | \(\dfrac{\mu_{0} I}{3 a}\) |
| 3. | \(\dfrac{2\mu_{0} I}{3 a}\) | 4. | \(0\) |
Consider six wires with the same current flowing through them as they enter or exit the page. Rank the magnetic field's line integral counterclockwise around each loop, going from most positive to most negative.
1. \(B>C>D>A\)
2. \(B>C=D>A\)
3. \(B>A>C=D\)
4. \(C>B=D>A\)
1. \(\frac{2}{\sqrt{3}} \left(\frac{\tau}{Bi}\right)\)
2. \(\frac{1}{\sqrt{3}} \frac{\tau}{Bi}\)
3. \(2 \left(\frac{\tau}{\sqrt{3} Bi} \right)^{\frac{1}{2}}\)
4. \(\frac{2}{\sqrt{3}} \left(\frac{\tau}{Bi} \right)^{\frac{1}{2}}\)
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