Answer the following. (a) Define the term 'electric flux' and write its dimensions. (b) A plane surface, in shape of a square of side 1 cm is placed in an electric field E = (100\ N/C )i such that the unit vector normal to the surface is given by n = 0.8i + 0.6k. Find the electric flux through the surface.

PhysicsCBSE Class 12 · Board exam 2024, set 55/5/1 · 3 marks · Short answer

CBSE Class 12 Physics 2024: question 23

Set in the CBSE Class 12 board exam of 2024, paper 55/5/1, section C, question 23, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 3 marks · Short answerElectric Charges and Fields

Answer the following.

(a)
Define the term 'electric flux' and write its dimensions.
0 marks
(b)
A plane surface, in shape of a square of side 1 cm is placed in an electric field $E = (100 \frac{N}{C}) \hat{i}$ such that the unit vector normal to the surface is given by $\overset{n}{^} = 0.8 \hat{i} + 0.6 \hat{k}$ . Find the electric flux through the surface.
0 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 55/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Flux is a dot product of the field with the area vector.

Hint 2

Only the î component of n̂ contributes; convert cm² to m².

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(a) Electric flux through a surface is a measure of the number of electric field lines crossing that surface normally.
Mathematically it is the surface integral of the field, $ϕ_{E} = \oint E \cdot d S$ (for a uniform field, $E \cdot A$ ).
1 mark
Dimensions: $[ϕ_{E}] = [E] [A] = [M L T^{- 3} A^{- 1}] [L^{2}] = [M L^{3} T^{- 3} A^{- 1}]$
½ mark
(b) Area: $A = (1 cm)^{2} = 1 0^{- 4} m^{2}$ , so $A = 1 0^{- 4} (0.8 \hat{i} + 0.6 \hat{k}) m^{2}$ .
½ mark
$ϕ_{E} = E \cdot A = (100 \hat{i}) \cdot (0.8 \hat{i} + 0.6 \hat{k}) \times 1 0^{- 4}$
½ mark
$ϕ_{E} = 80 \times 1 0^{- 4} = 8 \times 1 0^{- 3} N m^{2} C^{- 1}$
½ mark

Answer: (a) Dimensions [ML³T⁻³A⁻¹]; (b) φ = 8 × 10⁻³ N m² C⁻¹

Where the marks are

Correct definition of electric flux (1 mark)
Dimensions ML³T⁻³A⁻¹ (½ mark)
Area vector written as 10⁻⁴ n̂ m² (½ mark)
Sets up the dot product (½ mark)
Flux = 8 × 10⁻³ N m²/C (½ mark)

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Chapter: Electric Charges and Fields (notes, formulas, where marks are lost and every past question)

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CBSE Class 12 Physics 2024: question 23

Hints

Step-by-step solution

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