Two magnetic dipoles $X$ and $Y$ are placed at a separation $d$, with their axes perpendicular to each other. The dipole moment of $Y$ is twice that of $X$. A particle of charge $q$ is passing through their mid-point $P$, at angle $\theta = 45^o$ with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant ? ($d$ is much larger than the dimensions of the dipole)
Two magnetic dipoles $X$ and $Y$ are placed at a separation $d$, with their axes perpendicular to each other. The dipole moment of $Y$ is twice that of $X$. A particle of charge $q$ is passing through their mid-point $P$, at angle $\theta = 45^o$ with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant ? ($d$ is much larger than the dimensions of the dipole)
- [JEE MAIN 2019]
- A
$\left( {\frac{{{\mu _0}}}{{4\pi }}} \right)\frac{M}{{{{\left( {d/2} \right)}^3}}} \times {q^\upsilon }$
- B
$0$
- C
$\left( {\frac{{{\mu _0}}}{{4\pi }}} \right)\frac{2M}{{{{\left( {d/2} \right)}^3}}} \times {q^\upsilon }$
- D
$\sqrt 2 \left( {\frac{{{\mu _0}}}{{4\pi }}} \right)\frac{M}{{{{\left( {d/2} \right)}^3}}} \times {q^\upsilon }$
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- [AIIMS 2017]
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$(b)$ A magnetised needle in a uniform magnetic field experiences a torque but no net force. An iron nail near a bar magnet, however, experiences a force of attraction in addition to a torque. Why?
$(c)$ Must every magnetic configuration have a north pole and a south pole? What about the field due to a toroid?
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$(a)$ What happens if a bar magnet is cut into two pieces: $(i)$ transverse to its length, $(ii)$ along its length?
$(b)$ A magnetised needle in a uniform magnetic field experiences a torque but no net force. An iron nail near a bar magnet, however, experiences a force of attraction in addition to a torque. Why?
$(c)$ Must every magnetic configuration have a north pole and a south pole? What about the field due to a toroid?
$(d)$ Two identical looking iron bars $A$ and $B$ are given, one of which is definitely known to be magnetised. (We do not know which one.) How would one ascertain whether or not both are magnetised? If only one is magnetised, how does one ascertain which one? [Use nothing else but the bars $A$ and $B$.]