At an interface of dielectrics with permittivities 1, 2, field lines make angles 1, 2 to the normal as shown. With no free surface charge, which relation holds?

$\epsilon_1\sin\theta_1=\epsilon_2\sin\theta_2$

$\epsilon_1\cos\theta_1=\epsilon_2\cos\theta_2$

$\epsilon_1\tan\theta_1=\epsilon_2\tan\theta_2$

GATE 2020 PH – Question 23

Electromagnetic theory · Dielectrics and conductors · 1 mark · Multiple choice

At an interface of dielectrics with permittivities $\epsilon_1,\epsilon_2$, field lines make angles $\theta_1,\theta_2$ to the normal as shown. With no free surface charge, which relation holds?

$\epsilon_1\sin\theta_1=\epsilon_2\sin\theta_2$
$\epsilon_1\cos\theta_1=\epsilon_2\cos\theta_2$
$\epsilon_1\tan\theta_1=\epsilon_2\tan\theta_2$
$\epsilon_1\cot\theta_1=\epsilon_2\cot\theta_2$

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Correct answer: (D) $\epsilon_1\cot\theta_1=\epsilon_2\cot\theta_2$

Explanation

Tangential E is continuous, so $E_1\sin\theta_1=E_2\sin\theta_2$. Normal displacement is continuous, so $\epsilon_1E_1\cos\theta_1=\epsilon_2E_2\cos\theta_2$. Dividing the second relation by the first gives $\epsilon_1\cot\theta_1=\epsilon_2\cot\theta_2$, option D.

GATE 2020 PH – Question 23

Explanation

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