Moving Charges and Magnetism

A thin uniform wire $$AB$$ of unknown resistance is connected between points $$A$$ and $$B$$. $$AP$$ and $$QR$$ are thick conducting strips. A battery of unknown electromotive force. $$E$$ and a galvanometer (with a sliding jockey connected to it) are available. Connections are be made to find electromotive force, $$E$$, resistance of wire $$AB$$ and length of $$AB$$. The battery with the galvanometer way such that jockey when passes on wire $$AB$$ at distance $$80 \ cm$$ and $$120 \ cm$$ respectively from end $$A$$, galvanometer shows no deflection.

If one end of battery with galvanometer is connected to pt. $$R$$ and jockey is pressed on $$AB$$ at distance $$180 \ cm$$ from end $$A$$, the deflection  in galvanometer is zero then find:
You are asked to do an experiment to study the effect of magnetic field on charged particle. You take two long wires having resistance $$10\Omega$$ and $$25\Omega$$. Separated them by $$5 cm$$ and keep them parallel. The two are connected to a battery of $$100 V$$ as shown in Figure. The battery branch is kept quite far away from the two conductors. A proton is allowed to enter the plane of the wires directed towards the upper wire with a velocity 650 $$km /s$$ exactly in the middle of the wire.
Two long straight conducting wires with linear mass density $$'\lambda'$$ are suspended using cords so that both of them are horizontal and parallel to each other at a distance $$'d'$$ apart. The back ends of the wires are connected by a low resistance slack wire. A charged capacitor is now added across the wires such that its positive terminal is connected to far end and negative terminal is connected to near end as shown in figure. The capacitance of the capacitor is $$C$$. These connections are also made by slack wires. Assume that time to discharge is negligible. Initial charge on capacitor is $$Q_0$$.
The magnetic induction in vacuum at a plane surface of a magnetic is equal to $$B$$ and the vector $$\vec{B}$$ forms an angle $$\theta$$ with the normal $$\vec{n}$$ of the surface (figure shown above). The permeability of the magnetic is equal to $$\mu$$.
A non-conducting thin disc of radius $$R$$ charged uniformly over one side with surface density $$s$$ rotates about its axis with an angular velocity $$\omega$$.