MHT CET · Physics · Magnetic Effects of Current
A wire of length \(L\) carries current \(I\) along \(x\)-axis. A magnetic field \(\vec{B}=B_0(\hat{i}-\hat{j}-\hat{k}) T\) acts on the wire. The magnitude of magnetic force acting on the wire is
- A \(\frac{\mathrm{ILB}_0}{2}\)
- B \(\mathrm{ILB}_0\)
- C \(2 \mathrm{ILB}_0\)
- D \(\sqrt{2} \mathrm{ILB}_0\)
Answer & Solution
Correct Answer
(D) \(\sqrt{2} \mathrm{ILB}_0\)
Step-by-step Solution
Detailed explanation
\(\vec{l} \times \vec{B} = (L\hat{i}) \times B_0(\hat{i}-\hat{j}-\hat{k}) = LB_0(0 - \hat{k} - (-\hat{j})) = LB_0(\hat{j} - \hat{k})\) \(|\vec{l} \times \vec{B}| = |LB_0(\hat{j} - \hat{k})| = LB_0\sqrt{1^2 + (-1)^2} = LB_0\sqrt{2}\)
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