The electric field in a region is given as →E=(3ˆi+4ˆj+ˆk)N/C𝐸→=(3𝑖^+4𝑗^+𝑘^) N/C . The flux of this field linked with a square of surface area 10 cm2 kept parallel to x-z plane is
Question
The electric field in a region is given as →E=(3ˆi+4ˆj+ˆk)N/C𝐸→=(3𝑖^+4𝑗^+𝑘^) N/C . The flux of this field linked with a square of surface area 10 cm2 kept parallel to x-z plane is
Solution
The electric field is given as E = 3i + 4j + k N/C and the area is parallel to the x-z plane.
The electric flux (Φ) through a surface is given by the dot product of the electric field (E) and the area vector (A). The area vector is always perpendicular to the surface, and in this case, since the surface is parallel to the x-z plane, the area vector is along the y-axis.
So, the area vector A = 10 cm^2 * j = 0.001 m^2 * j (since 1 m^2 = 10,000 cm^2).
Now, we can calculate the electric flux as follows:
Φ = E . A = (3i + 4j + k) . (0.001j) = 30.0010 + 40.0011 + 10.0010 = 0.004 N.m^2/C
So, the flux of the field linked with the square is 0.004 N.m^2/C.
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