Why Show Torque as a Vector?

For an electric dipole in electric field torque=p x e(cross product).If torque is the direction of force then why we don't take its direction as clockwise or anticlockwise instead we prefer perpendicular to the plane containing p and e.What is the direction of the torque when its magnitude is zero?
- Nivedhika (age 16)
Namakkal,Tamil nadu,India

I think you're asking why we represent torque as a vector, like an arrow, rather than as a loop with arrows on it showing which way to go around. The same question could also be asked about angular momentum, since torque is just the rate of change of the angular momentum. The loop picture sounds more natural to represent a spinning motion and how it changes. 

The basic reason is that those little loops aren't one of the standard mathematical objects we are used to handling. We'd have to write down a new set of rules for how to add the loops together, and so forth. Also, they're harder to fit into pictures than arrows. Now it turns out that if we replace each little loop with an arrow, with the length of the arrow representing the amount of torque and the direction directly out of the plane of the loop, the physical rules for adding torques are exactly the same as the mathematical rules for adding the vectors those arrows stand for. So since all physics students have already learned about vectors and how to represent them with arrows, we just use that same way of picturing torques. We also use vectors for angular momentum.

Mike W.

(published on 11/12/2013)