Torque on a hammer conceptual question.

[bdh2991]

Homework Statement

If you are trying to loosen a stubborn screw from a piece
of wood with a screwdriver and fail, should you find a screwdriver for which
the handle is (a) longer or (b) fatter?

Homework Equations

\tau = r * F * sin(\theta)

The Attempt at a Solution

I guessed longer because i figured that the larger radius would mean that you have a larger torque and need less force than if the radius was short, however the correct answer is B. Can someone explain this to me please?

 

[haruspex]

Larger torque, yes, but you don't get that from a longer screwdriver.
When using a given screwdriver, the limiting factor is the tangential force you can apply around the handle. That in turn is limited by the torque you can exert from your arm, but more often it is limited before that by the static frictional force achieved by your grip (as the normal force) on the handle.
What equation would relate such a tangential force to the resultant torque?
(The free body diagram might look unlike anything you're familiar with. If it helps, consider the tangential force as lots of little forces scattered around the handle.)