Magnetic Effects & Magnetism

JEE Main level, numerical answer, medium

123 of 276

Question 123 of 276

An electron moves through a uniform magnetic field B⃗=B0i^+2B0j^T\vec{B}={B}_{0}\hat{i}+2{B}_{0}\hat{j}T. At a particular instant of time, the velocity of electron is u⃗=3i^+5j^ms−1\vec{u}=3\hat{i}+5\hat{j}m{s}^{-1}. If the magnetic force acting on electron is F⃗=5ek^N\vec{F}=5e\hat{k}N, where ee is the charge of electron, then the value of B0{B}_{0} is ____ TT.

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Answer: 5

Force acting on a charged particle under the magnetic field is given by, F⃗=q(v⃗×B⃗)\vec{F}=q\left(\vec{v}\times \vec{B}\right).
⇒5ek⏜=e(3i⏜+5j⏜)×(B0i⏜+2B0j⏜)\Rightarrow 5ek^{⏜}=e\left(3i^{⏜}+5j^{⏜}\right)\times \left({B}_{0}i^{⏜}+2{B}_{0}j^{⏜}\right)
⇒5ek⏜=e(6B0k⏜−5B0k⏜)\Rightarrow 5ek^{⏜}=e\left(6{B}_{0}k^{⏜}-5{B}_{0}k^{⏜}\right)
⇒B0=5T\Rightarrow {B}_{0}=5T

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