The potential (in volts) of a charge distribution is given by |
\[V(z)=30-5{{z}^{2}}\]for\[|z|\le 1m\] |
\[V(z)=35-10|z|\]for\[|z|\ge 1m.\] |
V(z) does not depend on x and y . If this potential is generated by a constant charge per unit volume \[{{\rho }_{0}},\](in units of \[{{\varepsilon }_{0}}\]) which is spread over certain region ,then choose the correct statement. [JEE ONLINE 09-04-2016] |
A) \[{{\rho }_{0}}=40{{\varepsilon }_{0}}\]in the entire region
B) \[{{\rho }_{0}}=20{{\varepsilon }_{0}}\] in the entire region
C) \[{{\rho }_{0}}=20{{\varepsilon }_{0}}\] for \[|z|\]in\[\le 1m\]and \[{{\rho }_{0}}=0\]else where
D) (d\[{{\rho }_{0}}=10{{\varepsilon }_{0}}\]for \[|z|\]in \[\le 1m\]and\[{{\rho }_{0}}=0\] else where
Correct Answer: D
Solution :
[d] \[|E=\left\{ \begin{matrix} 10zv/m & |z|\le 1m \\ 10v/m & |z|\ge 1m \\ \end{matrix} \right.\] |
If should be for a sheet lying in x.y plane of thickness z = 2m. |
For \[|z|\ge 1mE=\frac{\sigma }{2{{\in }_{0}}}=\frac{\rho (2)}{2{{\in }_{0}}}=\frac{\rho }{{{\in }_{0}}}=10\Rightarrow P=10{{\in }_{0}}\] |
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