Question

Electric field $\overrightarrow{E}=4t\hat{i}$ exists in space. Displacement current associated with a square of side a = 2cm with its plane perpendicular to $\overrightarrow{\epsilon }$ at t = 2 sec will be

• A. $28\times {10}^{-15}A$
• B. $112\times {10}^{-15}A$
• C. $14\times {10}^{-15}A$
• D. $7\times {10}^{-15}A$

Answer 1

The correct option is C $14\times {10}^{-15}A$

Displacement current $i_d={\epsilon }_0\frac{d\varphi }{dt}={\epsilon }_0\frac{d}{dt}(E.A)$
$i_d={\epsilon }_0\frac{d}{dt}4t.a^2={\epsilon }_0{a}^{2}4=8.8\times {10}^{-12}\times 4\times {10}^{-4}\times 4=14\times {10}^{-15}A$