An electric dipole $\pm 4$ $μ C$ is kept at co-ordinate points $(1, 0, 4)$ are kept at $(2, - 1, 5)$ , the electric field is given by $\to E = 20^i$ $N C^{- 1}$ . Calculate the torque on the dipole.

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Solution

$\to P = 4 μ C \times (^i -^j +^k)$
$\Rightarrow | \to P | = 4 \times 10^{- 6} \sqrt{1^{2} + 1^{2} + 1^{2}}$
$\to E = 20^i$
$\Rightarrow | \to E | = 20$
angle $cos θ = \frac{\to P \cdot \to E}{| \to P | | \to E |} = \frac{1}{\sqrt{3}}$
$\to τ = \to P \times \to E = | \to P | | \to E | sin θ$
$sin θ = \frac{2}{\sqrt{3}}$
$\Rightarrow τ = 4 \sqrt{3} \times 20 \times \frac{2}{\sqrt{3}} \times 10^{- 6}$
$\Rightarrow τ = 160 \times 10^{- 6}$ $N m$

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An electric dipole ±4 μC is kept at co-ordinate points (1,0,4) are kept at (2,−1,5), the electric field is given by →E=20^i NC−1. Calculate the torque on the dipole.

→P=4μC×(^i−^j+^k)⇒|→P|=4×10−6√12+12+12→E=20^i⇒|→E|=20angle cosθ=→P⋅→E|→P||→E|=1√3→τ=→P×→E=|→P||→E|sinθsinθ=2√3⇒τ=4√3×20×2√3×10−6⇒τ=160×10−6 Nm

An electric dipole $\pm 4$ $μ C$ is kept at co-ordinate points $(1, 0, 4)$ are kept at $(2, - 1, 5)$ , the electric field is given by $\to E = 20^i$ $N C^{- 1}$ . Calculate the torque on the dipole.