Solved Exercise/Numericals - Electric Field Intensity (E) - Line, Surface & Mixed Charge Configuration - 2.


Q.1 An infinite long uniform line charge is located at y = 3, z = 5. If ρL = 30 nC/m. Calculate the electric field at point (5, 6, 1).

Ans:

The electric field intensity (E) due to an infinite line charge is given as:


In this case, ρ = (6 – 3) ay + ρ(1 – 5)az = 3ay – 4az

Hence aρ = (3ay - 4az) / 5

Therefore E is,











Q.2 A uniform line charge density 20 nC lies on z axis between z = 1 and z = 3.
Find electric field intensity at point (4, 0, 0).
Ans:



Electric field due to a line charge density is given as:







In this case

R = 4 ax – z az

ar = (4 ax – z az) / (42 + z2)


Hence we have,













Q. 3 Two identical charges are located on the y axis at y = 3 and y = 9. At what point in space is the net electric field zero?
Ans:

As the both charges are on the y axis, the point at which the fields due to the two charges can cancel has to lie on the y-axis also. Since the two charges are identical, the point at which the net electric field will be zero is midway between them, i.e. at point (0, 6, 0)



Q.4 A point charge 100 pC is located at (4, 1, -3) while the x-axis carries charge 2 nC/m. If the plane z = 3 also carries charge 5nC / m2, find E at (1, 1, 1).
Ans:
Electric field at point (1, 1, 1) is given as:


















= (- 0.0216, 0, 0.0288) + (0, 18, 18) – 264.7 (0, 0, 1)

= - 0.0216 ax + 18ay – 264.7 az V/m


Q.5 Plane x + 2y = 5 carries charge ρs = 6 nC/m2. Determine E at (-1, 0, 1)?
Ans:

Let f (x, y) = x + 2y – 5

∇ f = ax + 2ay
A unit normal vector to any surface or plane is given as:











Now since (-1, 0, 1) lies below the plane, therefore Electric field is given as:















ALSO READ:

- Introduction To Electrostatics.

- Coulomb's law.

- Electric Field Intensity (E).

- Electric Lines Of Forces /Streamlines / Electric Flux (ψ) .

- Electric Flux Density (D).

- Electric Field Intensity Due To a Finite and Infinite Line Charge.

- Electric Field Intensity Due To a Infinite Sheet Charge.

- Electric Field Intensity Due To a Circular Ring Charge.

- Electric Field Intensity Due To a Circular Disk Charge.

- Numericals / Solved Examples - Electric Force and Field Intensity.

- Numericals / Solved Examples - Electric Field Intensity - Line, Surface and Mixed Charge Configuration.


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3 comments:

  1. sir plz hlp me in solving this que
    infinite line charge of p=5nc/m lie along +ve n -ve x and y axes
    1)(0,0,4)
    2)(0,3,4)

    ReplyDelete
  2. plz hlp me in solving this que
    infinite line charge is located on both +ve n -ve x and y axes
    a)(0,0,4)
    b)(0,3,4)

    ReplyDelete
  3. infinite long charge is located on +ve and -ve xy axes
    1)(0,0,4)
    2)(0,3,4)

    ReplyDelete