TS EAMCET · Physics · Magnetic Effects of Current
A charge \(q\) enters a region having electric field \(\mathbf{E}\) and magnetic field \(\mathbf{B}\) with velocity \(\mathbf{v}\). If it continues to move with the same velocity, then which of the following statement is not true
- A \(\mathrm{E} \cdot \mathrm{B}=0\)
- B \(\mathrm{E} \cdot \mathrm{v}=0\)
- C If \(\mathrm{v} \cdot \mathrm{B}=0\), then \(\mathrm{v}=\frac{\mathrm{E} \times \mathrm{B}}{\mathrm{B} \times \mathrm{B}}\)
- D \(v \times E=B\)
Answer & Solution
Correct Answer
(D) \(v \times E=B\)
Step-by-step Solution
Detailed explanation
Lorentz force on electron, \[ F=q(\mathbf{E}+\mathbf{v}+\mathbf{B}) \] For regular motion, \(F=0\) \[ \Rightarrow \quad \mathbf{E}+(\mathbf{v} \times \mathbf{B})=0 \] \(\Rightarrow \mathbf{E} \|(\mathbf{v} \times \mathbf{B})\), also \([\mathbf{v} \times \mathbf{B}\) is…
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