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Electrostatics question

2025 · 7 Apr · Shift 2 · Q60
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Electrostatics question

2025 · 7 Apr · Shift 2 · Q60

JEE MainPhysicsElectrostaticsMCQ+4 / −1
A dipole with two electric charges of 2 µC magnitude each, with separation distance 0.5 µm, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, it tends to realign in the direction due to a torque. The value of torque is:
  1. A
    2.5×10−9 Nm
  2. B
    2.5×10−12 Nm
  3. C
    5×10−3 Nm
  4. D
    5×10−9 Nm
View written solutionFree

Correct answer: D

  1. Given data
  • Charge magnitude on each end of dipole:
    q=2 μC=2×10−6 Cq = 2\,\mu C = 2\times 10^{-6}\,Cq=2μC=2×10−6C
  • Separation of charges:
    d=0.5 μm=0.5×10−6 md = 0.5\,\mu m = 0.5\times 10^{-6}\,md=0.5μm=0.5×10−6m
  • Potential difference across capacitor plates:
    V=5 VV = 5\,VV=5V
  • Separation between plates:
    l = 0.5\,mm = 0.5\times 10^{-3}\,m
  • Dipole rotated by:
    θ=30∘\theta = 30^\circθ=30∘
  1. Electric field between capacitor plates

For parallel plates, E=Vl=50.5×10−3=104 N/CE = \frac{V}{l} = \frac{5}{0.5\times 10^{-3}} = 10^4\,N/CE=lV​=0.5×10−35​=104N/C

  1. Dipole moment

Magnitude of dipole moment is p=qdp = qdp=qd

So, p=(2×10−6)(0.5×10−6)=1×10−12 C⋅mp = (2\times 10^{-6})(0.5\times 10^{-6}) = 1\times 10^{-12}\,C\cdot mp=(2×10−6)(0.5×10−6)=1×10−12C⋅m

  1. Torque on dipole

Torque on an electric dipole in uniform electric field is τ=pEsin⁡θ\tau = pE\sin\thetaτ=pEsinθ

Substitute values: τ=(1×10−12)(104)sin⁡30∘\tau = (1\times 10^{-12})(10^4)\sin 30^\circτ=(1×10−12)(104)sin30∘

Since sin⁡30∘=12\sin 30^\circ = \frac{1}{2}sin30∘=21​

Therefore, τ=(1×10−12)(104)×12\tau = (1\times 10^{-12})(10^4)\times \frac{1}{2}τ=(1×10−12)(104)×21​ τ=0.5×10−8\tau = 0.5\times 10^{-8}τ=0.5×10−8 τ=5×10−9 N m\tau = 5\times 10^{-9}\,N\,mτ=5×10−9Nm

  1. Match with options

τ=5×10−9 N m\boxed{\tau = 5\times 10^{-9}\,N\,m}τ=5×10−9Nm​

So the correct option is D.

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