CBSE Class 12 Board Examination

Chapter 1: Electric Charges and Fields

Summary

Matter carries an intrinsic property called electric charge, which exists in two kinds, positive and negative, and is conserved and quantised as \(q=ne\). Like charges repel and unlike charges attract through a force whose magnitude between two point charges in vacuum obeys Coulomb's law \(F=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1q_2}{r^2}\). To describe the influence a charge exerts on its surroundings we introduce the electric field \(\vec{E}=\vec{F}/q_0\), a vector quantity whose direction follows the force on a positive test charge. Field lines give a pictorial map of \(\vec{E}\): they start on positive and end on negative charges, never cross, and crowd together where the field is strong. An electric dipole, two equal and opposite charges separated by a small distance, has a dipole moment \(\vec{p}=q\,2\vec{a}\) and experiences a torque \(\vec{\tau}=\vec{p}\times\vec{E}\) in a uniform field. Electric flux \(\Phi=\oint\vec{E}\cdot d\vec{A}\) measures the field threading a surface, and Gauss's law states the net flux through any closed surface equals the enclosed charge divided by \(\varepsilon_0\). Gauss's law gives elegant results for symmetric distributions: the field of an infinite line, an infinite charged sheet, and a uniformly charged spherical shell.

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