Question:
Find out the surface charge density at the intersection of point \(x = 3\ \mathrm{m}\) plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.
Find out the surface charge density at the intersection of point \(x = 3\ \mathrm{m}\) plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.
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Find the field of the infinite line charge at distance 3 m, \(E = \frac{\lambda}{2\pi\varepsilon_0 r}\), and take \(\sigma = \varepsilon_0 E\).
Updated On: Nov 4, 2026
- \(0.424\ \mathrm{nC\,m^{-2}}\)
- \(4.0\ \mathrm{nC\,m^{-2}}\)
- \(47.88\ \mathrm{C/m}\)
- \(0.07\ \mathrm{nC\,m^{-2}}\)
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The Correct Option is A
Solution and Explanation
Field of an infinite line charge at distance \(r\): \(E = \frac{\lambda}{2\pi\varepsilon_0 r}\).
The flux density (surface charge density of the plane at that point) is \(\sigma = \varepsilon_0 E = \frac{\lambda}{2\pi r}\).
\(\sigma = \frac{8\ \mathrm{nC/m}}{2\pi\times 3\ \mathrm{m}} = \frac{8}{18.85}\ \mathrm{nC\,m^{-2}} = 0.424\ \mathrm{nC\,m^{-2}}\).
Answer: (1) \(0.424\ \mathrm{nC\,m^{-2}}\)
The flux density (surface charge density of the plane at that point) is \(\sigma = \varepsilon_0 E = \frac{\lambda}{2\pi r}\).
\(\sigma = \frac{8\ \mathrm{nC/m}}{2\pi\times 3\ \mathrm{m}} = \frac{8}{18.85}\ \mathrm{nC\,m^{-2}} = 0.424\ \mathrm{nC\,m^{-2}}\).
Answer: (1) \(0.424\ \mathrm{nC\,m^{-2}}\)
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