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AIIMS 2017
Exam
AIIMS
Year
2017
Subject
Physics
Chapter
Electrostatics

AIIMS 2017 · Physics · Electrostatics

In a certain region of space, electric field is along the z...

In a certain region of space, electric field is along the zz-direction throughout. The magnitude of electric field is however not constant, but increases uniformly along the positive zz-direction at the rate of 105 NC−1 m−110^5 \mathrm{~N} \mathrm{C}^{-1} \mathrm{~m}^{-1}. The force experienced by the system having a total dipole moment equal to 10−7Cm10^{-7} \mathrm{C} \mathrm{m} in the negative zz-direction isIn a certain region of space, electric field is along the z -direction throughout. The magnitude of electric field is

Options

  1. A−10−2 N-10^{-2} \mathrm{~N}
  2. B10−2 N10^{-2} \mathrm{~N}
  3. C10−4 N10^{-4} \mathrm{~N}
  4. D−10−4 N-10^{-4} \mathrm{~N}

Correct answer

A. −10−2 N-10^{-2} \mathrm{~N}

Step-by-step solution

Consider an electric dipole with −q-q charge at AA and +q+q charge at BB, placed along zz-axis, such that its dipole moment is in negative zz direction. i.e., pz=−10−7Cmp_{\mathrm{z}}=-10^{-7} \mathrm{Cm} The electric field is along positive direction of zz-axis, such that dEdz=105NC−1 m−1\frac{d E}{d z}=10^5 \mathrm{NC}^{-1} \mathrm{~m}^{-1} From, F=qdEF=q d E =(q×dz)×dEdz=pdEdz=(q \times d z) \times \frac{d E}{d z}=p \frac{d E}{d z} Force experienced by the system in the negative zz-direction, F=−p×(−dEdz)=10−7×(−105)=−10−2 NF=-p \times\left(-\frac{d E}{d z}\right)=10^{-7} \times\left(-10^5\right)=-10^{-2} \mathrm{~N} In a certain region of space, electric field is along the z -direction throughout. The magnitude of electric field is
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