Define magnetic flux through a plane surface placed in a uniform magnetic field. Write its formula, name its S

Example · Example 2

Q. Define magnetic flux through a plane surface placed in a uniform magnetic field. Write its formula, name its SI unit, and state the two situations in which the flux through a given surface is

(a) maximum and

(b) zero.

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✓ Free question

Concept understanding — Magnetic Flux

Definition. The magnetic flux $\Phi_B$ through an area A in a field $\vec B$ is the number of field lines passing normally through that area, formally the surface integral $\Phi_B=\int\vec B\cdot d\vec A$ over the whole area, with the integral's dot product picking out only the field component along each element's own outward normal. For the common special case of a FLAT area A in a UNIFORM field $\vec B$ , making a fixed angle $\theta$ with the area's normal, this reduces to

\Phi_B = BA\cos\theta

Extremes. Flux is MAXIMUM ( $\Phi_B=BA$ ) when the field is exactly along the area's normal ( $\theta=0^{\circ}$ , $\cos0^{\circ}=1$ ) -- i.e. when the field is perpendicular to the plane of the area itself. Flux is exactly ZERO when the field lies entirely IN the plane of the area ( $\theta=90^{\circ}$ , $\cos90^{\circ}=0$ ) -- i.e. when the area's normal is perpendicular to the field. A frequent source of numerical error is confusing these two angles: the angle a plane makes with the field, and the angle the plane's NORMAL makes with the field, always differ by exactly $90^{\circ}$ from each other.

Unit. The SI unit is the tesla-metre-squared (T m $^2$ ), given the named unit weber (Wb): $1\ \text{Wb}=1\ \text{T m}^2$ . Flux is the single quantity whose CHANGE, via Faraday's law, is responsible for every induced emf covered in this unit -- whether that change comes from a varying field strength, a varying enclosed area, or a varying relative orientation (section 4.4).

"Magnetic flux formula and unit weber" and "magnetic flux class 12 important questions" are frequently searched terms tied to the Electromagnetic Induction chapter of the NCERT/CBSE Class 12 Physics curriculum, since flux is the foundational quantity behind every Faraday's-law numerical asked in board exams, JEE Main and NEET. The angle-confusion trap flagged here, between the field-to-plane angle and the field-to-normal angle, is one of the most common scoring errors in flux-based exam problems.

Magnetic flux through a flat surface of area $A$ in a uniform field $\vec{B}$ is defined as $\Phi_B=\vec{B}\cdot\vec{A}=BA\cos\theta$ , where $\vec{A}$ is the area vector (magnitude $A$ , direction along the surface's normal) and $\theta$ is the angle between $\vec{B}$ and this normal. Since it is a dot product of two vectors, flux is a SCALAR. SI unit: weber (Wb), $1\ \text{Wb}=1\ \text{T}\,\text{m}^2$ .

Maximum flux. When the surface's plane is perpendicular to $\vec{B}$ , its normal is parallel to $\vec{B}$ , so $\theta=0^\circ$ , $\cos\theta=1$ , and $\Phi_B=BA$ (maximum possible value for the given $B$ and $A$ ).
Zero flux. When the surface's plane is parallel to $\vec{B}$ instead, its normal is perpendicular to $\vec{B}$ , so $\theta=90^\circ$ , $\cos\theta=0$ , and $\Phi_B=0$ -- no field lines cross the surface in this orientation at all.
✓Final answer
$\Phi_B=BA\cos\theta$

Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set SEM31 markMCQ
$Q. A square loop of side 1 m and resistance 1 Ω is placed in a magnetic field of 0\cdot5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is$
(a) 0·5 weber
(b) 1 weber
(c) 0 weber
(d) 2 weber
›Reveal solutionSolution

Magnetic flux φ = B·A·cos θ. The plane of the loop is perpendicular to B, so B is along the normal (θ = 0) and φ = BA = 0·5 × 1 = 0·5 Wb. Option (a).

Step 1 — area of the square loop: A = (1 m)² = 1 m².

Step 2 — orientation: 'plane of the loop perpendicular to B' means the field is along the area's normal, so the angle between B and the normal is 0° and cos θ = 1.

Step 3 — flux: φ = B A cos θ = 0·5 T × 1 m² × 1 = 0·5 Wb.

This flux definition underpins Faraday's law in the NCERT/CBSE Class 12 Physics chapter on Electromagnetic Induction.

✓Final answer
$(a) 0\cdot5 weber$
CBSE 2023Set ANNUAL1 markMCQ
$Q. The magnetic flux linked with a coil of N turns of area of cross-section A held with its plane parallel to the field B is$
(1) NAB
(2) NAB/2
(3) NAB/4
(4) zero
›Reveal solutionSolution

Magnetic flux depends on the angle between the field and the AREA VECTOR (normal to the coil), not the plane itself.

$\Phi = NAB\cos\theta$ , where $\theta$ is the angle between $\vec B$ and the normal $\hat n$ to the coil's plane. If the coil's plane is parallel to $\vec B$ , then the normal $\hat n$ is perpendicular to $\vec B$ , so $\theta=90^\circ$ and $\cos 90^\circ = 0$ .

✓Final answer
$(4) zero.$
CBSE 2023Set ANNUAL1 mark
$Q. Write the relation between weber and tesla units.$
›Reveal solutionSolution

Tesla is the unit of magnetic flux density (B), weber is the unit of magnetic flux (Φ = B·A), so weber equals tesla times square metre.

Magnetic flux $\Phi$ through a surface of area $A$ in a uniform field of magnetic flux density $B$ is:

$\Phi = B \cdot A$

Here $B$ is measured in tesla (T), the SI unit of magnetic flux density, and $\Phi$ is measured in weber (Wb), the SI unit of magnetic flux. Since $\Phi = BA$ , dimensionally:

$1\ \text{Wb} = 1\ \text{T} \times 1\ \text{m}^2$

Equivalently, $1\ \text{T} = 1\ \text{Wb}/\text{m}^2$ — tesla is weber per square metre.

✓Final answer
$1 weber = 1 tesla \times 1 m² (Wb = T\cdotm²), i.e. 1 T = 1 Wb/m².$
CBSE 2016Set ANNUAL1 markMCQ
$Q. Dimension of magnetic flux is$
(a) [ML²T⁻²A⁻¹]
(b) [MLT⁻¹A⁻²]
(c) [ML⁻¹TA⁻¹]
(d) [MT⁻¹A]
›Reveal solutionSolution

Magnetic flux Φ = B·A; working out the dimension of B from F = qvB and multiplying by area gives [ML²T⁻²A⁻¹].

From F = qvB, the dimension of B = [F]/([q][v]) = (MLT⁻²)/((AT)(LT⁻¹)) = MT⁻²A⁻¹.

Magnetic flux Φ = B×A (A = area, dimension L²):

[Φ] = (MT⁻²A⁻¹)(L²) = ML²T⁻²A⁻¹

✓Final answer
$(a) [ML²T⁻²A⁻¹].$

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Q.Define magnetic flux through a plane surface placed in a uniform magnetic field. Write its formula, name its SI unit, and state the two situations in which the flux through a given surface is

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