An electron moves through a uniform magnetic field B → = B 0 i ^ + 2 B 0 j ^ T . At a particular instant of time, the velocity of electron is u → = 3 i ^ + 5 j ^ m s - 1 . If the magnetic force acting on electron is F → = 5 e k ^ N , where e is the charge of electron, then the value of B 0 is ____ T .

Force acting on a charged particle under the magnetic field is given by, F → = q v → × B → . ⇒ 5 e k ⏜ = e 3 i ⏜ + 5 j ⏜ × B 0 i ⏜ + 2 B 0 j ⏜ ⇒ 5 e k ⏜ = e 6 B 0 k ⏜ - 5 B 0 k ⏜ ⇒ B 0 = 5 T

Physics - Magnetism Question with Solution | TestHub

PhysicsMagnetismMagnetic ForceHard2 minPYQ_2024

PhysicsHardnumerical

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 $\vec{u} = 3 \hat{i} + 5 \hat{j} m s^{- 1}$ . If the magnetic force acting on electron is $\vec{F} = 5 e \hat{k} N$ , where $e$ is the charge of electron, then the value of $B_{0}$ is ____ $T$ .

Answer:

5.00

Solution:

Force acting on a charged particle under the magnetic field is given by, $\vec{F} = q (\vec{v} \times \vec{B})$ .

$\Rightarrow 5 e \overset{⏜}{k} = e (3 \overset{⏜}{i} + 5 \overset{⏜}{j}) \times (B_{0} \overset{⏜}{i} + 2 B_{0} \overset{⏜}{j})$

$\Rightarrow 5 e \overset{⏜}{k} = e (6 B_{0} \overset{⏜}{k} - 5 B_{0} \overset{⏜}{k})$

$\Rightarrow B_{0} = 5 T$

Stream:JEESubject:PhysicsTopic:MagnetismSubtopic:Magnetic Force

⏱ 2mℹ️ Source: PYQ_2024

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