If the magnetic field intensity is \(3\hat{i}+4\hat{j}\) and the area vector is \(-2\hat{i}+\hat{j}\), then the magnetic flux associated with the area is:

Question

Question

Answer 1

CONCEPT:

Magnetic flux:

Magnetic flux is defined as the number of magnetic field lines passing through a given closed surface.
It provides the measurement of the total magnetic field that passes through a given surface area.
It is a scalar quantity.
The SI unit of magnetic flux is Weber (Wb).

Magnetic flux associated with any area is given as,

⇒ ϕ_B = BAcosθ

Where ϕB = magnetic flux, B = magnetic field intensity, A = area, and θ = angle between B and A

CALCULATION:

Given \(\vec{B}=3\hat{i}+4\hat{j}\) and \(\vec{A}=-2\hat{i}+\hat{j}\)

We know that the magnetic flux associated with any area is given as,

⇒ ϕB = BAcosθ

\(⇒ \phi_B=\vec{B}\cdot\vec{A}\)

\(⇒ \phi_B=(3\hat{i}+4\hat{j})\cdot(-2\hat{i}+\hat{j})\)

⇒ ϕB = -6 + 4

⇒ ϕB = - 2 Wb