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The electric field at 2R from the centre of a uniformly charged non-conducting sphere of radius R is E. The electric field at a distance R/2 from the centre will be ??a) Zero b) 2E c) 4E d) 16E
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The electric field at 2R from the centre of a uniformly charged non-co...
Explanation:
Let Q be the total charge of the sphere. Since the sphere is uniformly charged, the charge density is given by ρ = Q/(4/3πR^3).
Electric field at 2R from the centre:
Using Gauss’s law, we can find the electric field at a distance 2R from the centre of the sphere.
∫E.dA = Q/ε₀
Where ε₀ is the permittivity of free space. The electric field is constant over the Gaussian surface, which is a spherical surface of radius 2R.
E.4π(2R)^2 = Q/ε₀
E = Q/(4πε₀R^2)
E = ρ(4/3πR^3)/(4πε₀R^2) = ρR/(3ε₀)
E = (Q/(4/3πR^3))(R/(3ε₀)) = Q/(3πε₀R^2)
E = kQ/R^2
Where k = 1/(4πε₀) is the Coulomb constant.
Therefore, the electric field at a distance 2R from the centre of the sphere is E = kQ/R^2.
Electric field at R/2 from the centre:
Using the principle of superposition, we can find the electric field at a distance R/2 from the centre of the sphere.
Let P be a point at a distance R/2 from the centre of the sphere. We can divide the sphere into concentric shells of thickness dr and radius r, where r ranges from 0 to R.
The electric field due to each shell at point P is given by dE = k(dq)/r^2, where dq is the charge on the shell.
The total charge on the shell of radius r is Q(r) = (4/3)πr^3ρ = (4/3)πr^3(Q/(4/3πR^3)) = (r^3/R^3)Q.
The electric field due to the shell of radius r at point P is dE = k(dq)/r^2 = k(Q(r)/R^3)(r^2)/(R/2)^2 = 2kQ(r)/R^3.
The total electric field at point P is obtained by integrating over all the shells:
E = ∫dE = ∫(2kQ(r)/R^3)dr = (2k/R^3)∫Q(r)rdr = (2k/R^3)Q∫r^4dr/R^4 = (2k/R^3)Q(R^5/5R^4) = (2/5)(kQ/R^2).
Therefore, the electric field at a distance R/2 from the centre of the sphere is E = (2/5)(kQ/R^2) = (2/5)E = 0.4E.
Community Answer
The electric field at 2R from the centre of a uniformly charged non-co...
For outside formula is kq/r^2 nd in side kqr/R^3 after equating this ans will 2E
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The electric field at 2R from the centre of a uniformly charged non-conducting sphere of radius R is E. The electric field at a distance R/2 from the centre will be ??a) Zero b) 2E c) 4E d) 16E
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The electric field at 2R from the centre of a uniformly charged non-conducting sphere of radius R is E. The electric field at a distance R/2 from the centre will be ??a) Zero b) 2E c) 4E d) 16E for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The electric field at 2R from the centre of a uniformly charged non-conducting sphere of radius R is E. The electric field at a distance R/2 from the centre will be ??a) Zero b) 2E c) 4E d) 16E covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The electric field at 2R from the centre of a uniformly charged non-conducting sphere of radius R is E. The electric field at a distance R/2 from the centre will be ??a) Zero b) 2E c) 4E d) 16E.
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