---
title: "Line charge and sheet charge, find D"
subject: "Electromagnetism"
chapter: 2
key: "semester_3/electromagnetism:line-charge-and-sheet-find-d"
source: https://www.bctengineer.com/q/semester_3/electromagnetism/line-charge-and-sheet-find-d
site: BCT Engineering
---

# Line charge and sheet charge, find D

Electromagnetism · Chapter 2: Electric field

- Asked in: 2070 Chaitra, 6 marks
- Video: [Electric Field due to Point, Line & Surface charge | EMFT lecture](https://www.youtube.com/watch?v=xghSPIgqBmU) — CADDD Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electromagnetism/line-charge-and-sheet-find-d
- Whole chapter: https://www.bctengineer.com/md/semester_3/electromagnetism/chapter-2

## Question

Along the z-axis there is a uniform line of charge with ρ_L = 4π C/m and in the x = 1 plane there is a surface charge with ρ_s = 20 C/m². Find the electric flux density at (0.5, 0, 0).

## Short answer

D from the line charge is 4a_x C/m². From the sheet, D = −10a_x C/m². The total flux density at (0.5,0,0) is the sum: D = −6a_x C/m².

## Answer

Superpose the flux densities of the line charge (z-axis) and the sheet (plane x = 1) at the point (0.5, 0, 0).

#### Line charge on the z-axis, ρ_L = 4π C/m
D = ρ_L/(2πρ) a_ρ. The point is at ρ = 0.5 m on the +x side, so a_ρ = a_x.

```text
D_L = 4π/(2π × 0.5) a_x = 4 a_x  C/m²
```

#### Sheet at x = 1, ρ_s = 20 C/m²
D = (ρ_s/2) a_n, with a_n pointing from the sheet to the point. The point (x = 0.5) is on the side x < 1, so a_n = −a_x.

```text
D_S = (20/2)(−a_x) = −10 a_x  C/m²
```

#### Total
```text
D = D_L + D_S = 4 a_x − 10 a_x = −6 a_x  C/m²
```

**Answer: D = −6 a_x C/m²** at (0.5, 0, 0).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The line charge on the z-axis gives at (0.5, 0, 0):
   A. 8 a_x C/m²
   B. 4 a_x C/m²
   C. −4 a_x C/m²
   D. 2 a_x C/m²
   Answer: B. D = 4π/(2π × 0.5) = 4, along +a_x. (Key point: Line D)

2. The sheet at x = 1 gives D with magnitude:
   A. ρ_s/2 = 10 C/m²
   B. ρ_s = 20 C/m²
   C. ρ_s/4π
   D. 5 C/m²
   Answer: A. D = (ρ_s/2) a_n. (Key point: Sheet D)

3. At x = 0.5 the sheet's D points along:
   A. +a_x
   B. +a_y
   C. −a_z
   D. −a_x, away from the sheet
   Answer: D. The point is on the side x < 1, so away from the sheet is −a_x. (Key point: Sheet direction)

4. D at the point is:
   A. 14 a_x C/m²
   B. 6 a_x C/m²
   C. −6 a_x C/m²
   D. −14 a_x C/m²
   Answer: C. 4 − 10 = −6 a_x. (Key point: Total)

## Related in Electromagnetism

- [Potential due to sheet and line charge](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Asheet-and-line-charge-potential) — Electromagnetism, chapter 2
- [Sheet and line charge, E at origin](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Asheet-line-charge-e-origin) — Electromagnetism, chapter 2
- [Uniform line charge, find E at P](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Aline-charge-20nc-find-e-p) — Electromagnetism, chapter 2
- [Point charge and four line charges, D](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Apoint-and-four-line-charges-d) — Electromagnetism, chapter 2
- [Flux through sphere, two line charges](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Aflux-leaving-sphere-two-line-charges) — Electromagnetism, chapter 2
- [Line charge and point charge, find E](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Aline-and-point-charge-find-e) — Electromagnetism, chapter 2, asked 2×

## Related in other subjects

- [Field of charged rod along its axis](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Acharged-rod-field-along-axis) — Engineering Physics, chapter 7
- [Resistance of alloy sheet along length and thickness](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aresistivity-alloy-sheet-resistance) — Basic Electrical Engineering, chapter 1
- [Choice of flux density in transformer design](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Atransformer-flux-density-choice) — Electric Machine Design, chapter 3
- [True/False: magnetic loading and teeth flux density](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Atf-magnetic-loading-teeth) — Electric Machine Design, chapter 5