A potentiometer wire of length $4\ \text{m}$ and resistance $5\ \Omega$ is connected in series with a resistance of $992\ \Omega$ and a cell of e.m.f. $4\ \text{V}$ with internal resistance $3\ \Omega$. The length of $0.75\ \text{m}$ on potentiometer wire balances the e.m.f. of

By connecting a resistance of $980\ \Omega$ in series with a galvanometer, it is converted into a voltmeter of a certain range. When the resistance of $470\ \Omega$ is connected in series, the range is halved. The resistance of the galvanometer is

The region inside a current carrying toroid is filled with a material (Niobium) having susceptibility $\chi = 2.6 \times 10^{-5}$. The percentage increase in the magnetic field in the presence of Niobium over that without it, is

In the following figure, the magnitude of the magnetic field at point 'O' will be