Electric Charges and Fields
Class 12 Physics · Physics Part I · Chapter 1
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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.
Charge, conservation and quantisationCoulomb's law and superpositionElectric field and field linesElectric dipole and torqueElectric flux and Gauss's lawApplications of Gauss's law
Key terms
Quantisation of charge
Charge appears only in integral multiples of the elementary charge \(e\), so \(q=ne\).
Coulomb's law
The electrostatic force between two point charges varies as the product of charges and inversely as the square of separation.
Electric field
Force per unit positive test charge at a point, \(\vec{E}=\vec{F}/q_0\), measured in N/C.
Electric dipole moment
Vector \(\vec{p}=q\,2\vec{a}\) directed from the negative to the positive charge.
Electric flux
Scalar product of field and area summed over a surface, \(\Phi=\oint\vec{E}\cdot d\vec{A}\).
Gauss's law
Net flux through a closed surface equals the enclosed charge divided by \(\varepsilon_0\).
Extra questions & answers
Try one from this chapter
Electric charge is quantised. This means the total charge on a body is always: