KCET 2025 Physics Paper

To find the magnetic flux through a square loop of side 2 meters that lies in the Y−Z plane, given the magnetic field

→

B

=(5

^

i

+3

^

j

−4

^

k

)T, we proceed as follows:
Determine the area vector:
Since the loop is in the Y-Z plane, its area vector A is perpendicular to this plane and points along the Xaxis. The magnitude of the area vector is given by the area of the square, which is 2×2=4 square meters. The area vector is thus A=4

^

i

.
Calculate the magnetic flux:
The magnetic flux φ through the loop is given by the dot product of the magnetic field B and the area vector A :
φ=B⋅A=(5

^

i

+3

^

j

−4

^

k

)⋅4

^

i

Performing the dot product, we have:
φ=(5×4)+(3×0)+(−4×0)=20‌Wb
Thus, the magnitude of the magnetic flux through the square loop is 20 Wb .