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Electrostatic Potential And Capacitance

Question
CBSEENPH12039576

An electric dipole has a fixed dipole moment straight p with rightwards arrow on top, which makes angle θ with respect to the x-axis. When subjected to an electric field stack straight E subscript 1 with rightwards arrow on top space equals space straight E with rightwards arrow on top straight i with hat on top, it experiences a torque stack straight T subscript 1 with rightwards arrow on top space equals space τk. When subjected to another electric field stack straight E subscript 2 with rightwards arrow on top space equals space square root of 3 straight E subscript 1 space straight j with hat on top space space it experiences torque stack straight T subscript 2 with rightwards arrow on top space equals space minus space stack straight T subscript 1 with rightwards arrow on top. The angle θ is

  • 60°

  • 90°

  • 30°

  • 45°

Solution

A.

60°


From space straight tau with rightwards arrow on top space equals space straight p with rightwards arrow on top space straight x space straight E with rightwards arrow on top
straight tau straight k with hat on top space equals space straight tau straight k with hat on top space equals space left parenthesis straight p subscript straight x space straight i with hat on top space plus straight p subscript straight y straight j with hat on top right parenthesis space straight x space left parenthesis straight E straight i with hat on top space plus space square root of 3 straight E straight j with hat on top right parenthesis
space equals space straight p subscript straight x space straight X space square root of 3 straight E space straight k with hat on top space plus space straight p subscript straight y space straight E left parenthesis negative straight k with hat on top right parenthesis
0 space equals space straight E straight k with hat on top space left parenthesis square root of 3 straight p subscript straight x space minus space straight p subscript straight y right parenthesis
straight p subscript straight y over straight p subscript straight x space equals space square root of 3
therefore space tan space straight theta space equals space square root of 3
straight theta space equals space 60 to the power of degree

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