The magnetic field due to a current carrying circular loop of radius $$3$$ $$cm$$ at a point on the axis at a distance of $$4$$ $$cm$$ from the centre is $$54\,\mu T.$$ What will be its value at the center of loop?

In a uniform magnetic field of induction $$B$$ a wire in the form of a semicircle of radius $$r$$ rotates about the diameter of the circle with an angular frequency $$\omega .$$ The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $$R,$$ the mean power generated per period of rotation is

The electrochemical equivalent of a metal is $${3.35109^{ - 7}}$$ $$kg$$ per Coulomb. The mass of the metal liberated at the cathode when a $$3A$$ current is passed for $$2$$ seconds will be

The thermo $$emf$$ of a thermocouple varies with temperature $$\theta $$ of the hot junction as $$E = a\theta + b{\theta ^2}$$ in volts where the ratio $$a/b$$ is $${700^ \circ }C.$$ If the cold junction is kept at $${0^ \circ }C,$$ then the neutral temperature is