JEE Mains · Physics · STD 12 - Moving charges and magnetism
- JEE Mains 2024
- Hard
- Numerical
An electron moves through a uniform magnetic field \(\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T\). At a particular instant of time, the velocity of electron is \(\overrightarrow{\mathrm{u}}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}\). If the magnetic force acting on electron is \(\vec{F}=5 e\hat kN\), where \(e\) is the charge of electron, then the value of \(\mathrm{B}_0\) is _______\(\mathrm{T}\).
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(5\)
Step-by-step Solution
Detailed explanation
\(\vec{F}=q(\vec{v} \times \vec{B})\)
\(5 e \hat{k}=e(3 \hat{i}+5 \hat{j}) \times\left(B_0 \hat{i}+2 B_0 \hat{j}\right)\)
\(5 e \hat{k}=e\left(6 B_0 \hat{k}-5 B_0 \hat{k}\right)\)
\(\Rightarrow B_0=5 T\)
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