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A straight wire connected to a battery can jump sideways when it sits between the poles of a magnet. Nothing is pulling it along the wire. The push is perpendicular to the wire, and it only appears when current is flowing and the wire sits in a magnetic field. That sideways push is the motor effect, and it is the first step on the path from electricity to rotation.
You can think about the setup as three physical ingredients in the same region of space. There is a magnetic field produced by the magnets. There is an electric current in the wire produced by the battery. Then there is a mechanical force on the wire, which can make it move if it is free.
See the main directions in a typical motor effect setup.
A magnetic field is a physical field that tells you how strongly magnets act on moving electric charge at each point in space. Its standard symbol is , and its SI unit is the tesla (T). A larger means a stronger magnetic influence in that region, for the same current and geometry.
An electric current is the rate at which electric charge flows past a point in a circuit. Its standard symbol is , and its SI unit is the ampere (A). Current is not the same thing as voltage. Voltage is what drives charge to move around a loop. Current is the moving charge itself, measured as how much passes per second.
In the motor effect experiment, the magnets set up in the gap between their poles, and the battery drives a current through the wire in that same gap. The magnetic field does not need to change with time for the wire to feel a force. A steady field and a steady current are enough.
Current in a metal wire comes from many charged particles drifting along the wire. Each moving charge experiences a magnetic force that points sideways relative to its motion and the magnetic field. The wire is not a single charge, but the sideways forces on all those moving charges add up and push on the metal lattice. That is why the whole wire segment can move.
Orientation controls the effect. If the wire runs parallel to the magnetic field lines, the sideways push can drop to nearly zero. If the wire runs perpendicular to the field, the sideways push is largest. This is not because the current changes. It is because the magnetic field can only deflect moving charge when there is a sideways component to deflect.
A common wrong intuition is that the magnet pulls the wire toward the nearest pole. That feels right because magnets pull steel. Here the force is not an attraction to a pole. It reverses direction when you reverse the current, even though the magnet stays put.
Compare how wire orientation changes the force direction and size.