A charge of $$+1 \mathrm{C}$$ is moving with velocity $$\vec{V}=(2 \mathrm{i}+2 \mathrm{j}-\mathrm{k}) \mathrm{ms}^{-1}$$ through a region in which electric field $$\vec{E}=(\mathrm{i}+\mathrm{j}-3 \mathrm{k}) \quad \mathrm{NC}^{-1}$$ and magnetic field $$\vec{B}=(\mathrm{i}-2 \mathrm{j}+3 \mathrm{k}) \mathrm{T}$$ are present. The force experienced by the charge is

To increase the current sensitivity of a moving coil galvanometer by $$25 \%$$, its resistance is increased so that the new resistance becomes twice its initial resistance. By what factor does the voltage sensitivity change?

Current flows through uniform, square frames as shown in the figure. In which case is the magnetic field at the centre of the frame not zero?

Two similar coils $A$ and $B$ of radius '$$r$$' and number of turns '$$N$$' each are placed concentrically with their planes perpendicular to each other. If I and $$2 \mathrm{I}$$ are the respective currents passing through the coils then the net magnetic induction at the centre of the coils will be: