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The strength of a magnetic field can be measured as strength in a specific direction.
We can calculate the strength of a magnetic field along the field lines from measuring the strength in x,y,z direction separately and calculating it from this.

Is it possible to measure the same with a single sensor, instead of three?
Can a 3D compass needle measure the the force along its orientation, for example?

I am curious not only about existing sensors, but also about ones that could work in principle only, and can not practically be build.

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The energy density of the field is a measure of its magnitude. For example, if you discharge the field of a solenoid and make a spark, the spark is a measure of the magnitude of the field.

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