Question
Download Solution PDFCompute the cartesian components of the electric field at the point if the potential at any point is given by V = x (y2 - 4x2)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
V = x (y2 - 4x2)
Concept:
To calculate electric field from potential function, we use partial derivate wrt x, y and z respectively.
Formula:
Ex = -δV/δx,
Ey = -δV/δy,
Ez = -δV/δz
where δy/δx means partial derivative of y wrt x treating other variables as constant.
Calculation:
V = x (y2 - 4x2)
⇒ V = xy2 - 4x3
• Ex = -δV/δx
⇒ Ex = \(-\frac{\delta(xy^2 - 4x^3) }{\delta x}\)
= -(y2 - 12x2)
= 12x2 - y2
• Ey = -δV/δy
⇒ Ex = \(-\frac{\delta(xy^2 - 4x^3) }{\delta y}\)
= -2xy
• Ez = \(-\frac{\delta(xy^2 - 4x^3) }{\delta z}\)
= 0
∴ Ex = 12x2 - y2, Ey = -2xy, Ez = 0
Last updated on May 26, 2025
-> AAI ATC exam date 2025 will be notified soon.
-> AAI JE ATC recruitment 2025 application form has been released at the official website. The last date to apply for AAI ATC recruitment 2025 is May 24, 2025.
-> AAI JE ATC 2025 notification is released on 4th April 2025, along with the details of application dates, eligibility, and selection process.
-> Total number of 309 vacancies are announced for the AAI JE ATC 2025 recruitment.
-> This exam is going to be conducted for the post of Junior Executive (Air Traffic Control) in Airports Authority of India (AAI).
-> The Selection of the candidates is based on the Computer Based Test, Voice Test and Test for consumption of Psychoactive Substances.
-> The AAI JE ATC Salary 2025 will be in the pay scale of Rs 40,000-3%-1,40,000 (E-1).
-> Candidates can check the AAI JE ATC Previous Year Papers to check the difficulty level of the exam.
-> Applicants can also attend the AAI JE ATC Test Series which helps in the preparation.