# How can I determine a direction of force which is made by magnetic field and current with a wire? Fleming left hand rule seemingly not works at here

Please assume that the conductor of wire exists , and the current flows from below left to above right like shown in the above diagram.

As shown in the above diagram , the uniform magnetic fields are given .

I want to know the forces which act against the wire.

I tried to use the rule of Flemming left hand .

But this rule seemingly only be able to be used as an angle between a magnetic field and a current , is a right angle .

I know the below formula .

$$\boldsymbol{f}= l \left( \boldsymbol{I}\times\boldsymbol{B} \right)$$

Hence, the below is held .

$$\Vert \boldsymbol{f} \Vert = l \cdot \left(\Vert \boldsymbol{I} \Vert \cdot \Vert \boldsymbol{B} \Vert \cdot \sin^{}\left(\theta_{} \right) \right)$$

Just simply applying the above equation of magnitude can easily obtain the magnitude of total force which acts against the wire however how can I obtain the direction of the force vector?

I think the directions of it must be perpendicular against the directions of the magnetic fields but I don't know how to prove it so far.

I looked the page of wikipidea of cross product and found the below image .

Cited it from here

Moreover how can I determine the vectors of forces as the directions of the magnetic fields are reversed?

• Thank you. I will check it. Commented Aug 23, 2021 at 4:28