The dual of Faraday's Law is Ampere's Law but, while Faraday's Law is fundamental to the physics of an inductor, Ampere's Law is *not* fundamental to the physics of a capacitor.

Now, it is true that, in *circuit theory*, the capacitor and inductor are duals:

$$i_C = C\frac{dv_C}{dt} \leftrightarrow v_L = L \frac{di_L}{dt}$$

However, we have to be more careful outside the context of circuit theory.

In physics, the fundamental relationship

$$Q = CV$$

clearly requires the existence of electric charge and an electric scalar potential due to a conservative electric field. This equation relates electric charge and electric scalar potential.

The closest we can get to a dual of this is

$$\Phi = LI $$

which relates magnetic flux and electric current. *But magnetic flux is not the dual of electric charge*.

The missing ingredient here is the hypothetical *magnetic charge* (magnetic monopole) which is the dual of electric charge.* Were magnetic charge \$Q_m\$ (measured in webers) to exist, it would be a source or sink of a *conservative* magnetic field (measured in amperes per meter) and there would be an associated scalar magnetic potential (measured in amperes).

We could thus relate magnetic charge and magnetic scalar potential with a magnetic "capacitance" measured in henrys.

Further, we could relate electric flux to magnetic current (measured in volts) with an electric "inductance" measured in farads.

To summarize, while electric flux and magnetic flux are duals, and changing magnetic flux is fundamental to the physics of an inductor, changing electric flux is not fundamental to the physics of a capacitor. Indeed, it is the electric field itself, not the electric flux, that is fundamental.

*Assuming magnetic charge exists, Maxwell's equations become

$$\nabla \cdot \vec D = \rho_e$$

$$\nabla \cdot \vec B = \rho_m$$

$$\nabla \times \vec E = - (\vec J_m + \frac{\partial \vec B}{\partial t})$$

$$\nabla \times \vec H = \vec J_e + \frac{\partial \vec D}{\partial t}$$

It is technically true that very intense magnetic fields can do awful things to a human brain, but what you're asking about is current flow. In your example there is no return path for current flow, the circuit is not complete, and you are safe. If there was a second lead that could complete the circuit, then current could flow.

Of course, I should point out that if your example creates an extreme voltage, the path could possibly complete itself, through the air, in the form of an arc. Also, don't go thinking you can just put on thick rubber shoes and grab a high voltage line - the rubber forms a kind of capacitance, through which a lethal AC current can still flow to ground.

## Best Answer

This is one way of doing it. Ref

A normal transformer can't deal with DC currents. Therefore the operating principle of DC current probes is rather different from AC probes. Here also is the current carrying conductor the primary winding and is inserted through the core opening. There is also a secondary winding, but now it functions as a compensation coil. The core is provided with an air gap that holds a sensor, e.g. a hall-sensor, which measures the magnetic flux in the core.

The current in the primary wire will magnetize the core. This magnetic field is measured with the sensor and as a result of this, the control circuit runs a current through the compensation winding in a way that the magnetic flux in the core is kept zero. As a result of this the core will never be magnetized. The advantage is that the non-linear properties and hysteresis of both the core and the magnetic sensor have little influence on the measurement results.

Beside the described measurement circuit there is also demagnetization circuit. Before using the current probe the core must be degaussed without wires inserted in the core.

Gain can be increased with compensation turns ratio at the expense of bandwidth.

## Side Note

True RMS RF power meters work something like above, except instead of magnetic loop matching, they use a thermal resistor and using a bridge to compare RF heat with a DC heater for accurate measurements and obviously much lower bandwidth from thermal time constant, but very accurate.