Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

no clear is seen in the link. plzz explain again and try to answer every question. the question asked was 'Derive gauss law from coulomb law
Asked by haroonrashidgkp | 31 Mar, 2018, 02:08: PM
answered-by-expert Expert Answer
Let us consider a point charge +q at centre of a sphere of radius r. Let us consider a small area ΔS on the surface of sphere. By definition the electric flux ΔΦ passing through the surface ΔS is 
ΔΦ = E•ΔS..................(1)
Electric field E at a given point is the force experienced by a unit charge placed at that point. We can get the force experienced by a unit charge for a point on the surface from coulomb's law. Hence as per coulombs law E = begin mathsize 12px style fraction numerator q over denominator 4 pi epsilon subscript 0 r squared end fraction end style  , where r is radius of sphere.
hence begin mathsize 12px style capital delta ϕ space equals space fraction numerator q over denominator 4 pi epsilon subscript 0 r squared end fraction bold r with bold hat on top space times space bold increment bold italic S bold space bold space comma space w h e r e space bold r with bold hat on top space i s space u n i t space v e c t o r space a l o n g space t h e space r a d i u s end style
Normal to the area ΔS and unit radius vector are in same direction. Hence we can write begin mathsize 12px style capital delta ϕ space equals space fraction numerator q over denominator 4 pi epsilon subscript 0 r squared end fraction increment S bold space end style.............(2)
Total flux through the surface of sphere is begin mathsize 12px style surface integral increment ϕ space equals space surface integral E times increment S end style
To get the surface integral of flux over the surface area of the sphere, we sum up the flux given by equation (2) over the surface area of sphere.
hence begin mathsize 12px style surface integral bold italic E bold. bold increment bold italic S space equals space fraction numerator q over denominator 4 pi epsilon subscript 0 r squared end fraction cross times 4 pi space r squared space equals space q over epsilon subscript 0 end style
Hence Gauss's law is stated as begin mathsize 12px style surface integral bold italic E bold. bold increment bold italic S space equals space space q over epsilon subscript 0 end style
(1) Though we have used Spherical surface to derive Gauss's law, Gauss's law is valid for any closed surface
(2) If there are multiple charges, charge given in the right side of equation (3) is sum of all charges present inside the closed surface.
(3) the charges can be present anywhere inside the closed surface.
Answered by Thiyagarajan K | 31 Mar, 2018, 04:05: PM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 12-science - Physics
if breakdown voltage of each capacitor is 40v ,then maximum applied voltage Vmax will be
Asked by aishaisha091098 | 19 Apr, 2024, 04:54: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
explain
question image
Asked by ranadeb8090 | 19 Apr, 2024, 03:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
solve option e
question image
Asked by dasrituparna1999 | 13 Apr, 2024, 06:56: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
The number of moles in an elemental sample is just the ratio of the mass m to atomic mass 4. n= A The number of protons N, in an elemental sample is Z (atomic number) times the number of moles of Avogadro's number NA N=ZnN P A Copper has an atomic mass of 63.5 g/mole and 29 protons per atom. If such an atom were neutral, then it would have as many protons as electrons. If you remove electrons from a neutral state, then you get a net positive charge. Given a 54 gram ball of copper with a net charge of 2.2 µC, what fraction of the copper's electrons have been removed?
Asked by dasrituparna1999 | 12 Apr, 2024, 09:26: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
which answer is correct and most appropriate with explanation
question image
Asked by mishrigupta19319 | 08 Apr, 2024, 06:28: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
8212
question image
Asked by madhav9119887644 | 07 Apr, 2024, 08:10: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
ans the questions wit reason
question image
Asked by mishrigupta19319 | 07 Apr, 2024, 11:23: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
I don't know which concept and formula is used
question image
Asked by adityagalar2007 | 06 Apr, 2024, 01:06: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
what is the mass of the bidy
question image
Asked by amlanmcob | 06 Apr, 2024, 12:27: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
13./A point charge of 12 µC is located at the centre of a cube of side 1 m. Calculate the electric flux through each face of the cube. (H.S.S.C.E.1999~S) [Ans. 2.26\times10^{5}N~m^{2}C^{-1}]
Asked by hussain221man | 05 Apr, 2024, 08:44: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×