14.2.1 F=BIL

Just like a magnet, a current carrying conductor also experiences a magnetic force when placed in a magnetic field.

The magnitude of the magnetic force Fb exerted on long straight wire of length L carrying a current I placed perpendicular to a uniform magnetic field B is given by the formula

\displaystyle {{F}_{b}}=BIL

There is something very interesting about the direction of Fb. It is NOT in the direction of B. It is also NOT in the direction of I. Instead, it is in a third direction – the direction that is perpendicular to both B and I. To use the Fleming’s Left Hand Rule (FLHR), do the hand pistol (and shout “FBI”!), because your thumb, index finger and middle finger are pointing at Fb, B and I respectively.

Now, what if B and I are not perpendicular to each other? Well, if the magnetic field is parallel to the current,  then zero magnetic force is exerted on the wire. This tells us that only the component of B perpendicular to the current, \displaystyle {{B}_{\bot }}, exerts a force on the wire. So if B and I are misaligned by angle q, then

\displaystyle \begin{aligned}{{F}_{b}}&={{B}_{\bot }}IL\\&=(B\sin \theta )IL\\&=BIL\sin \theta \end{aligned}

Concept Test

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