Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Electrostatics question

2019 · 12 Jan · Shift 1 · Q61
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Electrostatics
  5. /2019 · 12 Jan · Shift 1 · Q61

Electrostatics question

2019 · 12 Jan · Shift 1 · Q61

JEE MainPhysicsElectrostaticsMCQ+4 / −1
Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure : JEE Main 2019 (Online) 12th January Morning Slot Physics - Electrostatics Question 196 English
  1. A
    2qℓj^2q\ell \widehat j2qℓj​
  2. B
    (qℓ)i^+j^2\left( {q\ell } \right){{\widehat i + \widehat j} \over {\sqrt 2 }}(qℓ)2​i+j​​
  3. C
    3 qℓj^−i^2\sqrt 3 \,q\ell {{\widehat j - \widehat i} \over {\sqrt 2 }}3​qℓ2​j​−i​
  4. D
    −3 qℓj^- \sqrt 3 \,q\ell \widehat j−3​qℓj​
View written solutionFree

Correct answer: D

  1. Use the definition of dipole moment

For a system of point charges,

p⃗=∑iqir⃗i\vec p = \sum_i q_i \vec r_ip​=i∑​qi​ri​

where r⃗i\vec r_iri​ is the position vector of each charge with respect to the chosen origin.

  1. Take the geometry of the equilateral triangle

Let the side of the equilateral triangle be ℓ\ellℓ.

For an equilateral triangle, the height is

h=32ℓh = \frac{\sqrt{3}}{2}\ellh=23​​ℓ

From the standard figure for this question, the two equal positive charges at the base and one negative charge at the top give a net charge zero, so the dipole moment is origin-independent.

Choose origin at the midpoint of the base, with:

  • base along the xxx-axis,
  • upward direction along j^\hat jj^​.

Then coordinates are:

  • left base vertex: (−ℓ2,0)\left(-\frac{\ell}{2},0\right)(−2ℓ​,0) with charge +q+q+q
  • right base vertex: (ℓ2,0)\left(\frac{\ell}{2},0\right)(2ℓ​,0) with charge +q+q+q
  • top vertex: (0,32ℓ)\left(0,\frac{\sqrt3}{2}\ell\right)(0,23​​ℓ) with charge −2q-2q−2q
  1. Compute contribution of each charge

For the two base charges:

q(−ℓ2i^)+q(ℓ2i^)=0q\left(-\frac{\ell}{2}\hat i\right) + q\left(\frac{\ell}{2}\hat i\right)=0q(−2ℓ​i^)+q(2ℓ​i^)=0

Their xxx-components cancel, and they have no yyy-component.

For the top charge:

(−2q)(32ℓj^)=−3 qℓ j^(-2q)\left(\frac{\sqrt3}{2}\ell\hat j\right) = -\sqrt3\,q\ell\,\hat j(−2q)(23​​ℓj^​)=−3​qℓj^​

Thus,

p⃗=−3 qℓ j^\vec p = -\sqrt3\,q\ell\,\hat jp​=−3​qℓj^​
  1. Match with the options

This corresponds to

−3 qℓ j^-\sqrt3\,q\ell\,\hat j−3​qℓj^​

which is Option D.

  1. Comparison with stored correct answer

Stored correct answer: D

Our derived answer: D

So they agree.

PreviousNext

More from Electrostatics

  • There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V…2019 · MCQ
  • A charge Q is placed at a distance a/2 above the center of the square surface of edge a as shown in the figure. The electric flux through the square surface is Includes diagram2018 · MCQ
  • A body of mass M and charge q is connected to spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be at x=0, with an amplitude A. An electric field E is applied along the x…2018 · MCQ
  • A solid ball of radius R has a charge density ρ given by ρ=ρ o (1 −Rr​) for 0 ≤ r ≤ R. The electric field outside the ball is :2018 · MCQ
  • Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between theis F. A third identical conducting sphere, C, is uncharged. Sphere C is first touhed…2018 · MCQ
  • Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, −σ and +σ respectively. The potential of shell B is :2018 · MCQ
  • There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at P, in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere…2017 · MCQ
  • Four closed surfaces and corresponding charge distributions are shown below. Let the respective electric fluxes through the surfaces be Φ1​,Φ2​,Φ3​ and Φ4​. Then : Includes diagram2017 · MCQ