$4.$ Figure $2($a$)$ shows a uniform solid cylindrical shaft $\backslash ($ A B C D $\backslash )$ of length $\backslash (3$ L $\backslash )$ and diameter $\backslash ($ d $\backslash )$ that is built in to rigid walls at $\backslash ($ A $\backslash )$ and $\backslash ($ D $\backslash ).$ A pointer is attached to the shaft at $\backslash ($ B $\backslash )$ and a torque $\backslash ($ T $\backslash )$ is applied at $\backslash ($ C $\backslash ).$ A section through the shaft at $\backslash ($ B $\backslash )$ is shown in Figure $2($b$).$ Find the deflection $\backslash (\backslash$Delta $\backslash )$ of the end of the pointer as a function of the $\backslash ($ T$,$ L$,$ d$,$ c $\backslash )$ and the shear modulus of the material $\backslash ($ G $\backslash ).$