X P Q Y is a vertical smooth long loop having a total resistance R where P X is parallel to Q Y and separation between them is l. A constant magnetic…

A thin half ring of radius $35$ cm is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at centre of the half ring is $100$ V/m, then the value of $Q$ is _______ nC. ($\epsilon_o = 8.85 \times 10^{-12}$ C$^2$/Nm$^2$ and $\pi = 3.14$)

A Wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances $\left(R_{1}=R_{2}=R_{3}=R_{4}\right)$. When $R_{3}$ resistance is heated to some temperature, its resistance value has gone up by $10 \%$. The potential difference $\left(V_{a}-V_{b}\right)$ (after $R_{3}$ is heated) is $\_\_\_\_$ V. 

An inductor of inductance $10$ mH having resistance of $100\,\Omega$ is connected to battery of E.M.F. $1.0$ V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is $2$ mA and $4$ mA is _______. 

A moving coil of galvanometer when shunted with $2\,\Omega$ resistance gives a full scale deflection for a current of $500$ mA. When a resistance of $470\,\Omega$ is connected in series it gives a full scale deflection for $10$ V potential applied on it. The value of resistance of galvanometer coil is __________ $\Omega$.

A current carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest. The particle moves along the axis of solenoid. If $g$ is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :