Balancing point of a potentiometer shifts from a length of 60 cm to 40 cm by shunting the cell with a $4 \Omega$ resistance. What is the internal resistance of the cell?
A current $I=5 \mathrm{~A}$ flows along a thin wire shaped as shown in figure. The radius of curved part of the wire is equal to $R=100 \mathrm{~mm}$, the angle $2 \phi=90^{\circ}$. The magnitude of magnetic field at the point $O$ is approximately
$$ \left(\text { use, } \frac{\mu_0}{4 \pi}=10^{-7} \mathrm{~T} \mathrm{~mA}^{-1}\right) $$

A toroid has a core (non-ferro magnetic) of inner radius 24 cm and outer radius 26 cm around which 2000 turns of a wire is wound. If the current in the wire is 12 A , the magnetic field inside the core of the toroid is
A planet has magnetic dipole moment of $27 \times 10^{22} \mathrm{~A}-\mathrm{m}^2$. If the radius of the planet is 300 km , what would be the magnetic field at its equator? $\left(\right.$ use,$\left.\frac{\mu}{4 \pi}=10^{-7}\right)$
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