A uniformly charged semicircular arc of radius '$$r$$' has linear charge density '$$\lambda$$'. The electric field at its centre is ( $$\varepsilon_0=$$ permittivity of free space)

A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same temperature of $$200^{\circ} \mathrm{C}$$. When these are left in a room.

For emission of light, a light emitting diode (LED) is

A solenoid of length $$0.4 \mathrm{~m}$$ and having 500 turns of wire carries a current $$3 \mathrm{~A}$$. A thin coil having 10 turns of wire and radius $$0.1 \mathrm{~m}$$ carries current $$0.4 \mathrm{~A}$$. the torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid is $$\left(\mu_0=4 \pi \times 10^{-7}\right.$$ SI units, $$\left.\pi^2=10\right)\left(\sin 90^{\circ}=1\right)$$