Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Questions  >  The potential of a uniformly charged line wit... Start Learning for Free
The potential of a uniformly charged line with density λ is given by,
λ/(2πε) ln(b/a). State True/False. 
  • a)
    True
  • b)
    False
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The potential of a uniformly charged line with density λ is giv...
Answer: a
Explanation: The electric field intensity is given by, E = λ/(2πεr)
Vab = -∫ E.dr = -∫ λ/(2πεr). On integrating from b to a, we get λ/(2πε) ln(b/a).
View all questions of this test
Most Upvoted Answer
The potential of a uniformly charged line with density λ is giv...
Explanation:

Uniformly Charged Line Potential:
- The potential of a uniformly charged line with density λ is given by V = λ/(2πε) ln(b/a), where ε is the permittivity of the medium, a is the inner radius, and b is the outer radius of the charged line.

True Statement:
- The statement given in the question, λ/(2πε) ln(b/a), is true.

Explanation:
- The potential of a uniformly charged line is directly proportional to the charge density λ and the natural logarithm of the ratio of the outer radius (b) to the inner radius (a). This relationship is derived from the formula for the potential of a charged line.

Mathematical Interpretation:
- The expression λ/(2πε) ln(b/a) represents the potential at a point outside the charged line due to the distribution of charge along the line. The natural logarithm term accounts for the variation in potential with distance from the line.

Significance of the Result:
- Understanding the potential of a uniformly charged line is crucial in analyzing the electric field and energy distribution in systems involving line charges. This result provides a quantitative measure of the potential at different points around the charged line.

Application in Electrical Engineering:
- In electrical engineering, the concept of potential due to line charges is utilized in the design and analysis of transmission lines, antennas, and other systems involving linear charge distributions. The potential calculation helps engineers optimize the performance and efficiency of electrical systems.

Conclusion:
- The expression for the potential of a uniformly charged line, λ/(2πε) ln(b/a), is a fundamental result in electrostatics that finds widespread application in electrical engineering and related fields. Understanding this relationship is essential for solving problems involving line charges and electric potentials.
Explore Courses for Electrical Engineering (EE) exam

Similar Electrical Engineering (EE) Doubts

it depends on the length of the conductor the capacitance of the line is proportional to the length of the transmission line their effect is negligible on the performance of short having a length less than 80 km and low voltage transmission accidents of the transmission line along with the conductances forms the shunted mittens the conductance and the transmission line is because of the leakage over the surface of the conductor considered a line consisting of two conductors and be each of radius are the distance between the conductors being Des shown in the diagram below minus the potential difference between the conductors and via's work QA charge on conductor QB charge on conductor vvab pencil difference between conductor and the Epsilon minus absolute primitivity QA plus QV = 0 so that QA equals QB - equals DBA equals data equals DB equals our substituting these values and voltage equation we get the capacitance between the conductors is cab is referred to as lying to line capacitance if the two conductors are in VR oppositely charge then the potential difference between them is zero then the potential of each conductor is given by one half bath the capacitance between each conductor and point of zero potential and is capacitive CN is called the capacitance to neut or capacitance to ground capacitance cab is the combination of two equal capacity and VN series thus capacitance to neutral is twice the capacitance between the conductors IE CN equals to Cave the absolute primitivity Epsilon is given by Epsilon equals epsilono Epsilon are where epsilano is the permittivity of the free space and Epsilon or is the relative primitivity of the medium prayer capacitance reactants between one conductor and neutral capacitance of the symmetrical three phase line let a balanced system of voltage be applied to a symmetrical three-phase line shown below the phasor diagram of the three phase line with equilateral spacing is shown below take the voltage of conductor to neutral as a reference phaser the potential difference between conductor and we can be written the similarly potential difference between conductors and sea is on adding equations one and two we get also combining equation three and four from equation 6 and 7 the line to neutral capacitance the capacitance of symmetrical three phase line is same as that of the two wire line Related: Capacitance of Transmission Lines?

Top Courses for Electrical Engineering (EE)

The potential of a uniformly charged line with density λ is given by,λ/(2πε) ln(b/a). State True/False.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?
Question Description
The potential of a uniformly charged line with density λ is given by,λ/(2πε) ln(b/a). State True/False.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The potential of a uniformly charged line with density λ is given by,λ/(2πε) ln(b/a). State True/False.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The potential of a uniformly charged line with density λ is given by,λ/(2πε) ln(b/a). State True/False.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The potential of a uniformly charged line with density λ is given by,λ/(2πε) ln(b/a). State True/False.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE). Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of The potential of a uniformly charged line with density λ is given by,λ/(2πε) ln(b/a). State True/False.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The potential of a uniformly charged line with density λ is given by,λ/(2πε) ln(b/a). State True/False.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The potential of a uniformly charged line with density λ is given by,λ/(2πε) ln(b/a). State True/False.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The potential of a uniformly charged line with density λ is given by,λ/(2πε) ln(b/a). State True/False.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The potential of a uniformly charged line with density λ is given by,λ/(2πε) ln(b/a). State True/False.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev