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Q. No.Two short identical bar-magnets are placed on the \(x\)-axis at \(x=+1\) and \(x=-1,\) with their magnetic axes along the \(+x\) direction. As one moves along the \(y\)-axis,
| 1. | the \(y\)-component of the magnetic field \(=0\) |
| 2. | the \(x\)-component of the magnetic field \(=0\) |
| 3. | the \(x\)-component of the magnetic field is zero, only at the origin. |
| 4. | the \(y\)-component of the magnetic field is zero, only at the origin. |
Subtopic: Â Magnetic Field & Field Lines |
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Two short identical bar-magnets are placed on the \(x\)-axis at \(x=+1\) and \(-1,\) with their magnetic axes along the \(+x\) direction. The \(x\)-component of the magnetic field is plotted as one moves along the \(y\)-axis.
Which one is the correct graph?
Which one is the correct graph?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Â Magnetic Field & Field Lines |
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The magnetic field components due to a short magnet (dipole moment: \(m\)) at a point \(P\) are \(B_1,B_2\) along and perpendicular to the magnetic axis:
\(B_1=\dfrac{\mu_0}{4\pi}\dfrac{m}{r^3}(3\cos^2\theta-1)\\ B_2=\dfrac{\mu_0}{4\pi}\dfrac{m}{r^3}(3\sin\theta\cos\theta)\)
where, \(r=OP=\) the distance of \(P\) from the magnet's centre & \(\theta\) is the angle made by \(OP\) with the axis.
Two short identical bar magnets are placed at the two vertices \(B,C\) of the base \(BC,\) of the equilateral triangle \(\triangle ABC,\) with their axis parallel to the altitude. The magnetic field at the centre \(O\) of the triangle has the magnitude \((OB=r)\):
\(B_1=\dfrac{\mu_0}{4\pi}\dfrac{m}{r^3}(3\cos^2\theta-1)\\ B_2=\dfrac{\mu_0}{4\pi}\dfrac{m}{r^3}(3\sin\theta\cos\theta)\)
where, \(r=OP=\) the distance of \(P\) from the magnet's centre & \(\theta\) is the angle made by \(OP\) with the axis.
Two short identical bar magnets are placed at the two vertices \(B,C\) of the base \(BC,\) of the equilateral triangle \(\triangle ABC,\) with their axis parallel to the altitude. The magnetic field at the centre \(O\) of the triangle has the magnitude \((OB=r)\):
| 1. | \(\left(\dfrac{\mu_0}{4\pi}\dfrac{m}{r^3}\right)\cdot\dfrac{1}{4}\) |
| 2. | \(\left(\dfrac{\mu_0}{4\pi}\dfrac{m}{r^3}\right)\cdot\dfrac{1}{2}\) |
| 3. | \(\left(\dfrac{\mu_0}{4\pi}\dfrac{m}{r^3}\right)\cdot\dfrac{5}{4}\) |
| 4. | \(\left(\dfrac{\mu_0}{4\pi}\dfrac{m}{r^3}\right)\cdot\dfrac{5}{2}\) |
Subtopic: Â Analogy between Electrostatics & Magnetostatics |Â Magnetic Field & Field Lines |
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