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Electric Charge and Field Physics Electric Charge and Field Physics Class 12th

A uniformly charged disc of radius R having surface charge density $σ$ is placed in the xy plane with its centre at the origin. Find the electric field intensity along the z-axis at a distance Z from origin:-

Option 1 -

$E = \frac{σ}{2 ε_{0}} (1 + \frac{Z}{{(Z^{2} + R^{2})}^{1 / 2}})$

Option 2 -

$E = \frac{σ}{2 ε_{0}} (1 - \frac{Z}{{(Z^{2} + R^{2})}^{1 / 2}})$

Option 3 -

$E = \frac{2 ε_{0}}{σ} (\frac{1}{{(Z^{2} + R^{2})}^{1 / 2}} + Z)$

Option 4 -

$E = \frac{σ}{2 ε_{0}} (\frac{1}{(Z^{2} + R^{2})} + \frac{1}{Z^{2}})$

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

dA = 2r dr

$d q = σ \times 2 π r d r$

$\Rightarrow E = \int_{0}^{R} \frac{k d q z}{{(z^{2} + r^{2})}^{\frac{3}{2}}}$

$\Rightarrow E = \frac{σ}{2 ε_{0}} [1 - \frac{z}{\sqrt[]{R^{2} + z^{2}}}]$

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A uniformly charged disc of radius R having surface charge density $σ$ is placed in the xy plane with its centre at the origin. Find the electric field intensity along the z-axis at a distance Z from origin:-

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A uniformly charged disc of radius R having surface charge density σ is placed in the xy plane with its centre at the origin. Find the electric field intensity along the z-axis at a distance Z from origin:-

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A uniformly charged disc of radius R having surface charge density $σ$ is placed in the xy plane with its centre at the origin. Find the electric field intensity along the z-axis at a distance Z from origin:-