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

The ratio of magnetic field at the centre of the current carrying circular loop and its magnetic moment is '$x$'. When both the current and radius are tripled, then the ratio will be

In the circuit shown, when the current '$i$' is $3\text{A}$ and increasing at the rate of $1\text{A/s}$ the measurement of the potential difference between A and B is $12\ \text{V}$. But when the same current $3\text{A}$ is decreasing at the rate of $1\text{A/s}$, the measured potential difference $V_{AB}$ between A and B is $6\text{V}$. The value of 'R' in the circuit is

Two coils have a mutual inductance of $0.005\ \text{H}$. The current changes in the first coil according to equation $I = I_0\sin\omega t$, where $I_0 = 10\ \text{A}$ and $\omega = 60\pi\ \text{rad s}^{-1}$. The maximum values of e.m.f. in the second coil in volt will be