Electric Charges And Fields

Question

State Gauss's law in electrostatics. Use this law to derive an expression for the electric field due to an infinitely long straight wire of linear charge density A cm^–1.

Solution

Gauss’s law in electrostatics: It states that total electric flux over the closed surface S is

\frac{1}{ε_{0}}

times the total charge (q) contained in side S.

∴

ϕ_{E} = \oint_{s} \vec{E} . \vec{d s} = \frac{q}{ε_{0}}

Electric field due to an infinitely long straight wire.
Let us consider an infinitely long line charge having linear charge density

λ

. Assume a cylindrical Gaussian surface of radius r and length 1 coaxial with the line charge.

By symmetry, the electric field E has same magnitude at each point of the curved surface S₁ and is directed radially outward. So angle at surfaces between

\vec{{dS}_{1}} and {\vec{E}}_{1}

is zero, and angle of

\vec{{dS}_{2}}, \vec{{dS}_{3}}

with

\vec{E}

S_{2} and S_{3}

are

90 °

.

Total flux through the cylindrical surface,

\oint \vec{E} . \vec{ds} = \oint_{S_{1}} \vec{E} . \vec{{dS}_{1}} + \oint_{S_{2}} \vec{E .} \vec{{dS}_{2}} + \oint_{S_{3}} \vec{E} . \vec{{dS}_{3}}

= \oint_{S_{1}} {EdS}_{1} . \cos 0 ° + \oint_{S_{2}} {EdS}_{2} . \cos 90 ° + \oint_{S_{3}} {EdS}_{3} . \cos 90 ° = E \oint {dS}_{1} = E \times 2 πrl

Since λ is the charge per unit length and l is the length of the wire.
Thus, the charge enclosed

q = λl

According to Gaussian law,

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

State Gauss's law in electrostatics. Use this law to derive an expression for the electric field due to an infinitely long straight wire of linear charge density A cm^–1.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

State Gauss's law in electrostatics. Use this law to derive an expression for the electric field due to an infinitely long straight wire of linear charge density A cm–1.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

State Gauss's law in electrostatics. Use this law to derive an expression for the electric field due to an infinitely long straight wire of linear charge density A cm^–1.

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?