An electric field is given as E = 6y2z i + 12xyz j + 6xy2 k. An incremental path is given by dl = -3 i + 5 j – 2 k mm. The work done in moving a 2mC charge along the path if the location of the path is at p(0,2,5) is (in Joule)

To find the work done in moving a charge (q) along an incremental path (mathbf{dl}) in an electric field (mathbf{E}), the formula used is:

[ dW = q mathbf{E} cdot mathbf{dl} ]

Given:

– The electric field (mathbf{E} = 6y^2z mathbf{i} + 12xyz mathbf{j} + 6xy^2 mathbf{k}).

– The incremental path (mathbf{dl} = -3 mathbf{i} + 5 mathbf{j} – 2 mathbf{k}) mm, or converting to meters (since the electric field is in standard SI units) gives us (mathbf{dl} = -0.003 mathbf{i} + 0.005 mathbf{j} – 0.002 mathbf{k}) meters.

– The charge (q = 2 mC = 2 times 10^{-3} C).

– The location of the path is at (p(0,2,5)).

First, evaluate the electric field (mathbf{E}) at point (p(0,2,5)):

[ mathbf{E}(0,2,5) = 6(2)^2(5) mathbf{i} +