The magnitude of electric field intensity at point B ( 2 , 0 , 0 ) due to a dipole of dipole moment p → = i ^ + 3 j ^ kept at origin is (assume that the point B is at a large distance from the dipole and K = 1 4 π ε 0 )

Let p → = i ^ + 3 j ^ = p 1 → + p 2 → Therefore p 1 → = i ^ and p 2 → = 3 j ^ Field due to p 1 → at point B , E 1 = 2 × K 2 3 = K 4 Field due to p 2 → at point B , E 2 = K × 3 8 E n e t = E 1 2 + E 2 2 E n e t = K 2 16 + K 2 × 3 64 E n e t = 7 K 8

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PhysicsElectrostaticsdipoleEasy2 minPYQ_2020

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The magnitude of electric field intensity at point $B$ $(2, 0, 0)$ due to a dipole of dipole moment $\vec{p} = \hat{i} + \sqrt{3} \hat{j}$ kept at origin is (assume that the point $B$ is at a large distance from the dipole and $K = \frac{1}{4 π ε_{0}}$ )

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Answer:

Solution:

Let $\vec{p} = \hat{i} + \sqrt{3} \hat{j} = \vec{p_{1}} + \vec{p_{2}}$

Therefore $\vec{p_{1}} = \hat{i}$ and $\vec{p_{2}} = \sqrt{3} \hat{j}$

Field due to $\vec{p_{1}}$ at point $B$ ,

$E_{1} = \frac{2 \times K}{2^{3}} = \frac{K}{4}$

Field due to $\vec{p_{2}}$ at point $B$ ,

$E_{2} = \frac{K \times \sqrt{3}}{8}$

$E_{n e t} = \sqrt{E_{1}^{2} + E_{2}^{2}}$

$E_{n e t} = \sqrt{\frac{K^{2}}{16} + \frac{K^{2} \times 3}{64}}$

$E_{n e t} = \frac{\sqrt{7} K}{8}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:ElectrostaticsSubtopic:dipole

⏱ 2mℹ️ Source: PYQ_2020

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