Force on a Current Carrying Wire

$$F=\sum q\hat{v}\times \hat{B}$$

• Sum of all charges

$$\hat{F}=I\hat{l}\times \hat{B}$$

• Little L = Length of wire in B field, in the same direction as I (Meters)
• I = Current (Amps)
• B = Magnetic Field (Teslas)

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Torque

$$\tau =IAB$$

τ = Torque A = Area of the loop B = Magnetic Field

• This is true for any loop!

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Rotational Motion

• Rotation is done by interaction in between a charged wire and a magnetic field.

• Work is being done here, however, it is not being done by the magnetic force. The electric potential is doing the work on the object.

For a smaller torque, you can take

$$\tau =IABsin\theta$$

But, this can also be defined as

Torque up = Counterclockwise motion Torque down = Clockwise Motion