Question

An electric dipole having dipole moment (4 x 10-9) C-m is placed at origin along x-axis. What uniform electric field (in N/m) should be
applied along x-axis so that we get a equipotential spherical surface of radius 3m centred at origin?​

Answer 1

Answer:

1.33

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Answer 2

Answer:

The uniform electric field that should be applied along the x-axis is 1.332 N/m.

Explanation:

Given,

The dipole moment of an electric dipole (p) is 4 × 10⁻⁹ Cm

The radius of the equipotential spherical surface (r) is 3 m.

To find,

Uniform electric field (E) along the x-axis.

concept,

The radius(r) of the equipotential sphere enclosing the dipole (p) with uniform electric field (E) parallel to dipole moment is:

$r =(\frac{p}{4\pi\epsilon_0E})^{1/3}$

Calculation,

$r =(\frac{p}{4\pi\epsilon_0E})^{1/3}$

$\implies E = \frac{p}{4\pi \epsilon_0r^3}$

Here π = 3.14, ε₀ = 8.85 × 10⁻¹² F/m.

$\implies E = \frac{4 \times 10^{-9}}{4 \times 3.14 \times 8.85 \times 10^{-12}\times 3^3} N/m$

⇒ E = 1.332 N/m

therefore, the uniform electric field that should be applied along the x-axis is 1.332 N/m.

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