A conductor carrying a current in a magnetic field experiences a force given by the Lorentz equation.  It might be written q v * B where the velocity and the magnetic fields are vectors and their product is a vector cross product.  In terms of current the charge  is carried through a distance L in time t, and the current is the charge per time so the force is  I L * B where again the vector cross product comes in and the current is I. How must the wire be oriented in the magnetic field so that it does not experience a force at all?     There is no direction in which the force is zero.     The wire has to be parallel to the field with the current going opposite to the field.     The wire has to be parallel to the field with the current going in either direction in the wire.     The wire has to be perpendicular to the field

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Chapter1: Units, Trigonometry. And Vectors
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A conductor carrying a current in a magnetic field experiences a force given by the Lorentz equation.  It might be written

q v * B

where the velocity and the magnetic fields are vectors and their product is a vector cross product.  In terms of current the charge  is carried through a distance L in time t, and the current is the charge per time so the force is 

I L * B

where again the vector cross product comes in and the current is I.

How must the wire be oriented in the magnetic field so that it does not experience a force at all?

   

There is no direction in which the force is zero.

   

The wire has to be parallel to the field with the current going opposite to the field.

   

The wire has to be parallel to the field with the current going in either direction in the wire.

   

The wire has to be perpendicular to the field

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