Question

The external work required to slowly rotate a dipole of dipole moment 1C-m in uniform electric field of magnitude 20 V/m from stable equilibrium state to unstable equilibrium state is​

Answer 1

Answer:

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Explanation:

P=3×10

−8

Cm;E=10

4

N/C

At stable equilibrium (θ

1

)=0

∘

At unstable equilibrium (θ

2

)=180

∘

Work done in a rotating dipole is given by:

W=PE(cosθ

1

−cosθ

2

)=(3×10

−8

)(10

4

)[cos0

∘

−cos180

∘

]=3×10

−4

[1−(−1)]

W=6×10

−4

J.

Answer 2

Concept:

Equilibrium is defined as a stable situation or balance where opposing forces cancel out each other and where no changes are occurring.

Given:

The dipole moment is $1C/m$.

The uniform electric field of magnitude $20V/m$.

Find:

The external work done to slowly rotate a dipole from a stable equilibrium state to an unstable equilibrium state.

Solution:

The dipole moment, $p=1C/m$.

Electric field,  $E=20V/m$.

At stable equilibrium, $\theta _1=0^o$

At unstable equilibrium, $\theta _2=180^o$

Work done in a rotating dipole is given as:

$W=pE(cos(\theta _1)-cos(\theta _2))$

$W=1(20)(cos(0^o)-cos(180^o))$

$W=20(1-(-1))J\\W=40J$

The external work required to slowly rotate a dipole of dipole moment $1C/m$ in uniform electric field of magnitude $20V/m$ from a stable equilibrium state to unstable equilibrium state is​ $40J$.

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