6. A uniform positive charge distribution lies on the y axis as
shown below in red. Determine
the x and y components of the electric
field at a point P at a distance x to the right of the origin.
Take the
linear charge density to be lambda which is given by Q/L where Q is the total
charge and L is
the length of the charge distribution. Hint: write the
vectors, r, r’ and u in i,j,k notation and use
the
formula:
Figure 1:
Figure 2: 
| --> | assume(x>0,k>0,%lambda>0,L>0); |
| --> | dE_x(yp):=k*%lambda*x*(x^2+yp^2)^(-3/2); |
| --> | dE_y(yp):=-k*%lambda*yp*(x^2+yp^2)^(-3/2); |
| --> | integrate(dE_x(yp), yp, -L,0); |
| --> | integrate(dE_y(yp), yp, -L,0); |
| --> | E_y(x,k,la,L):=k*la*(1/x-1/(x^2+L^2)); |
| --> | wxplot2d([E_y(x,1,1,1)], [x,0,5], [y,0,20])$ |
| --> | E_x(x,k,la,L):=k*la*L/x/(x^2+L^2)^(1/2); |
| --> | wxplot2d([E_x(x,1,1,1)], [x,0,5], [y,0,20])$ |
