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KCET · Physics · Magnetic Effects of Current

A square loop of side 2 m lies in the \(Y-Z\) plane in a region having a magnetic field \(\vec{B}=(5 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}) \mathrm{T}\). The magnitude of magnetic flux through the square loop is

  1. A 20 Wb
  2. B 12 Wb
  3. C 16 Wb
  4. D 10 Wb
Verified Solution

Answer & Solution

Correct Answer

(A) 20 Wb

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \overline{\mathrm{A}}=(2 \times 2) \hat{\mathrm{i}} \quad \text { [as loop is in y-z plane] } \\ & =4 \hat{\mathrm{i}} \\ & \overline{\mathrm{B}}=5 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}} \mathrm{T} \\ & \therefore \phi=\overline{\mathrm{B}} \cdot \overline{\mathrm{A}}=(5 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}) \cdot 4 \hat{\mathrm{i}} \\ & =20 \mathrm{~Wb}\end{aligned}\)