GATE EC 2003 Electromagnetics Solution Q 1

GATE EC 2003 Electromagnetics Solution Q 1

If the electric field intensity is given by \overrightarrow E=\left(xu_x+yu_y+zu_z\right)Volt/m the potential difference between X(2,0,0) and Y(1,2,3) is

a) +1 Volt

b) -1 Volt

c) +5 Volt

d) +6 Volt

Ans- c)

Explanation

\begin{array}{l}V=-\int\overrightarrow E\cdot\overrightarrow{dl}\\\;\;\;=-\left[\int\limits_1^2xdx{\overrightarrow u}_x+\int\limits_2^0ydy{\overrightarrow u}_y+\int\limits_3^0zdz{\overrightarrow u}_z\right]\end{array} =-\left{\left.\frac{x^2}2\right|_1^2+\left.\frac{y^2}2\right|_2^0+\left.\frac{z^2}2\right|_3^0\right} \begin{array}{l}=-\frac12\left[2^2-1^2+0^2-2^2+0^2-3^2\right]\\=-\frac12\times-10=5V\end{array}

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