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2. Electric Potential and Capacitance
easy
જો $V\,\, = \,\, - 5x\,\, + \,\,3y\,\, + \,\,\sqrt {15} \,z\,$ હોય તો ${\text{E(x, y, z) = }}.....unit$
A
$8$
B
$6.7$
C
$7.7$
D
$7$
Solution
$\vec E\, = \,\, – \left[ {\frac{{\partial V}}{{\partial x}}\hat i\,\, + \,\,\frac{{\partial V}}{{\partial y}}\,\hat j\,\, + \,\,\frac{{\partial V}}{{\partial z}}\,\,\hat k} \right]\,\, = \, – ( – 5\,\,\hat i\,\, + \,\,3\,\,\hat j\,\, + \,\,\sqrt {15} \,\,\hat k)\,\,\,$
$ \Rightarrow \,\,|\hat E|\,\, = \,\,\sqrt {25\,\, + \,\,9\,\, + \,\,15} \,\, = \,\,\sqrt {49} \,\, = \,\,7\,$ યુનિટ
Standard 12
Physics
