A rod of length *L* lies along
the *x* axis with its left end at the origin. It
has a nonuniform charge
density *λ* = *α**x*,
where *α* is a positive constant.

Calculate the electric potential at point *B* ,
which lies on the perpendicular bisector of the rod a
distance *b* above the *x* axis.
(Use the following as
necessary: *α*, *k*_{e}, *L*, *b*,
and *d*.)

Community Answer

Consider the potential at a point p which coordinates x and y The contribution dV(X,Y) due to a segment dx ' of the charged rod is,{:[dV=(k_(e)dx^(')dx^('))/(sqrt((x^(')-x)^(2)+y^(2)))],[V=k_(e)alphaint_(0)^(L)(x^(')dx^('))/(sqrt((x^(')-x)^(2)+y^(2)))]:}Sub x^(')-x=u{:[V=k_(e)alphaint_(-x)^(-x+L)((u+x)du)/(sqrt(u^(2)+y^(2)))],[=k_(e)alphaint_(-x)^(-x+L)(xdu)/(sqrt(u^(2)+y^(2)))+k_(e)alphaint_(-x)^(-x+2)(udu)/(sqrt(u^(2)+y^(2)) ... See the full answer