A composite slab is prepared b pasting two plates of thicknesses L₁ and L₂ and thermal conductivities K₁ and K₂. The slabs have equal cross-sectional area. Find the equivalent conductivity of the slab.

1. \( {K}_{eq}{=}\frac{{L}_{1}{+}{L}_{2}}{\frac{{L}_{1}}{{K}_{1}}{+}\frac{{L}_{2}}{{K}_{2}}}\)
2. \( {K}_{eq}{=}\frac{{L}_{1}{+}{L}_{2}}{{K}_{1}{K}_{2}}\)
3. \( {K}_{eq}{=}\frac{{L}_{1}}{{K}_{1}{+}{K}_{2}}{+}\frac{{L}_{2}}{{K}_{1}{+}{K}_{2}}\)
4. \( {K}_{eq}{=}\frac{{L}_{1}{L}_{2}}{{L}_{1}{+}{L}_{2}}\)

Three long wires, each carrying current i are placed parallel to each other. The distance between I and II is 3d, between II and III is 4 d and between III and I is 5d. Magnetic field at side of wire II is 

1. $\frac{5{\mathrm{\mu }}_0\mathrm{i}}{24\mathrm{\pi d}}$

2. $\frac{10{\mathrm{\mu }}_0\mathrm{i}}{24\mathrm{\pi d}}$

3. $\frac{15{\mathrm{\mu }}_0\mathrm{i}}{24\mathrm{\pi d}}$

4. $\frac{20{\mathrm{\mu }}_0\mathrm{i}}{24\mathrm{\pi d}}$

In the following diagrams, a particle with small charge – q is free to move up or down, but not sideways near a larger fixed charge Q. The small charge is in equilibrium because in the positions shown, the electrical upward force is equal to the weight of the particle. Which statement is true? 

1. In figure a, -q is in stable equilibrium.

2. In figure a, -q is in neutral equilibrium.

3. In figure b, -q is in stable equilibrium.

4. Neither in fig(a) nor in fig(b) , q is in stable equilibrium.