B_X and B_Y are the magnetic fields at the centre of two coils X and Y respectively each carrying equal current. If coil X has 200 turns and 20 cm radius and coil Y has 400 turns and 20 cm radius, the ratio of B_X and B_Y is:

What is the formula for the force per unit length between two parallel current-carrying conductors?

A charge particle is moving in uniform magnetic field $\left(2\widehat{i}+3\widehat{j}\right)$ T. If it has an acceleration of $\left(\alpha \widehat{i}-4\widehat{j}\right)m/s^2$ , then the value of will be:

A wire $A$ , bent in the shape of an arc of a circle, carrying a current of $2\mathrm{A}$ and having radius $2\mathrm{c}\mathrm{m}$ and another wire $B$ , also bent in the shape of arc of a circle, carrying a current of $3\mathrm{A}$ and having radius of $4\mathrm{c}\mathrm{m}$ , are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre $O$ is:

The specific heat of water $=4200\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ and the latent heat of ice $=3.4\times {10}^5\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}$ . 100 grams of ice at $0^{\circ }\mathrm{C}$ is placed in $200\mathrm{g}$ of water at ${25}^{\circ }\mathrm{C}$ . The amount of ice that will melt as the temperature of water reaches $0^{\circ }\mathrm{C}$ is close to (in grams):