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2. Electric Potential and Capacitance
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વિદ્યુતસ્થિતિમાન $V = 4{x^2}\,volt$ છે.તો $(1m,\,0,\,2m)$ બિંદુ પર વિદ્યુતક્ષેત્ર કેટલું લાગે?
A
$8$ ૠણ $X$ - દિશામાં
B
$8$ ધન $X$ - દિશામાં
C
$16$ ૠણ $X$ - દિશામાં
D
$16$ ધન $Z$ - દિશામાં
(IIT-1992)
Solution
(a) The electric potential $V\,(x,y,z) = 4{x^2}\,volt$
Now $\overrightarrow E = – \,\left( {\hat i\frac{{\partial V}}{{\partial x}} + \hat j\frac{{\partial V}}{{\partial y}} + \hat k\frac{{\partial V}}{{\partial z}}} \right)$
Now $\frac{{\partial V}}{{\partial x}} = 8x,\,\frac{{\partial V}}{{\partial y}} = 0$ and $\frac{{\partial V}}{{\partial z}} = 0$
Hence $\overrightarrow E = – \,8x\hat i$, so at point ($1\,m, 0, 2\,m$)
$\overrightarrow E = – \,8\hat i\,\,volt/metre$ or $8$ along negative $X-$ axis.
Standard 12
Physics
