Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5
Banner 6

Q.

State ‘Gauss 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 λ cm-1.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away
An Intiative by Sri Chaitanya

answer is 1.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Gauss’s law in electrostatics: It states that “the total electric flux over the surface S in vacuum is 1ε0 times the total charge (q).

contained in side S   ϕE=SE.dS=qε0

Question Image

Electric field due to an infinitely long straight wire: Consider an infinitely long straight-line charge having linear charge density X to determine its electric field at distance r. Consider a cylindrical Gaussian surface of radius r and length l coaxial with the charge. By symmetry, the electric field E has same magnitude at each point of the curved surface S1 and is directed radially outward.
Total flux through the cylindrical surface,

E.dS=s1E.dS1+s2E.dS2+Es3.dS3                =s1EdS1 cos0°+s2EdS2cos 90°+s3EdS3cos 90°                =EdS1=E×2πrl As λ is the charge per unit length and l is the length of the wire, so charge enclosed is,    q=λl By Gauss's theorem :     E.dS1=qε0        E×2 πrl=λlε0  E=λ2πε0r  

Watch 3-min video & get full concept clarity

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon