# How does voltage affect a magnetic field?

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Jul 3, 2014

A magnetic field is a phenomenon that can occur in one of two ways: it is induced by a current carrying wire, or it is generated naturally by the charge arrangement in a ferrous material. That said, voltage is not exactly directly related to a magnetic field. However, because current is a result of a voltage in a circuit, fluctuations in applied voltages could potentially cause simultaneous changes in the strength of a magnetic field surrounding a wire. For many materials, voltage and current are related by Ohm's law which states:

$V = I R$
where $V$ represents the voltage [volts], $I$ is the current [amps], and $R$ is the resistance in the circuit [Ohms].

For a long, straight wire, Ampere's law (in its simplest form) states:

$B = \setminus \frac{{\mu}_{0} I}{2 \pi r}$

where ${\mu}_{0}$ is the magnetic constant, $I$ is the current in the wire, and $r$ is the distance between the wire and the point in question.

From this, it can be see that if resistance remains constant in the circuit, when voltage increases, current must also increase. Since the strength of the magnetic field is directly related to the current in the wire, the magnitude of the magnetic field would increase with an increase in voltage in the circuit.

In terms of electromagnetic induction, the EMF or voltage generated by a generator is proportional to the time rate of change of the magnetic flux through the current loop experiencing the EMF. This relationship is called Faraday's law:

$\setminus \varepsilon = - N \setminus \frac{d \setminus {\Phi}_{B}}{\mathrm{dt}}$

where $\setminus \varepsilon$ is the emf (generally measured in volts), $N$ is the number of turns in the coil, and $\setminus {\Phi}_{B}$ is the magnetic flux passing through the loop.

In terms of dimensional analysis, from this you can see that a volt is a weber per second, or a tesla meter squared per second.

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