Find linear charge density if infinite line charges produce a field of 9 x 104 and the distance is 2 cm.
Solution and Explanation
Electric field due to infinite line charge is given by:
\(E=\frac{\lambda}{2\pi\epsilon_0d}\)
⇒ \(\lambda=2\pi\epsilon_0Ed\) …….....(1)
Where λ is the linear charge density and d is the perpendicular distance of a point from the infinite line charge.
Step 2: Substituting the values
∵\(\frac{1}{4\pi\epsilon_0}=9\times10^9Nm^2C^{-2}\)
⇒ \(2\pi\epsilon_0=\frac{1}{18\times10^9Nm^2C^{-2}}\)
From Eq (1): \(\lambda=\frac{1\times9\times10^4NC^{-1}\times0.02}{18\times10^9Nm^2C^{-2}}=10^{-7}Cm^{-1}\)
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Concepts Used:
Electrostatic Potential
The electrostatic potential is also known as the electric field potential, electric potential, or potential drop is defined as “The amount of work that is done in order to move a unit charge from a reference point to a specific point inside the field without producing an acceleration.”
SI Unit of Electrostatic Potential:
SI unit of electrostatic potential - volt
Other units - statvolt
Symbol of electrostatic potential - V or φ
Dimensional formula - ML2T3I-1
Electric Potential Formula:
The electric potential energy of the system is given by the following formula:
U = 1/(4πεº) × [q1q2/d]
Where q1 and q2 are the two charges that are separated by the distance d.
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