A solenoid is oriented end-on so that its opening is perpendicular to the circuit containing the two light bulbs as drawn in figure $C_1.$ For figure $C_2$ and $C_3,$ a shorting wire of negligible resistance is added as shown. Assume that the magnetic field from the solenoid, shown coming out of the plane of the page, decreases uniformly with time at the same rate for each circuit. Rank the circuits for the brightness of the bulb labeled $R_1$ from brightest to dimmest.
Diffcult
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$\Delta \mathrm{V}$ across the $\mathrm{R}_{1}$ is more then more brighter.
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For a positively charged particle moving in a $x-y$ plane initially along the $x$-axis, there is a sudden change in its path due to the presence of electric and/or magnetic fields beyond $P$. The curved path is shown in the $x-y$ plane and is found to be non-circular. Which one of the following combinations is possible
Assertion $(A):$ A wire bent into an irregular shape with the points $P$ and $Q$ fixed. If a current $I$ passed through the wire, then the area enclosed by the irregular portion of the wire increases.
Reason $(R):$ Opposite currents carrying wires repel each other.
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