An electron moves through a uniform magnetic field B = B₀i + 2B₀j T. At a particular instant of time, the velocity of electron is u = 3i + 5j m/s. If the magnetic force acting on electron is F = 5ek N, where e is the charge of electron, then the value of B₀ is _________ T. Numerical answer type. Work it out, then open the answer.

Answer: 5. F = -e( u× B) u× B = (3 i + 5 j)×(B₀ i + 2B₀ j) = (6B₀ - 5B₀) k = B₀ k -eB₀ k = 5e k ⇒ B₀ = -5 T Magnitude of B₀ is 5 T.

An electron moves through a uniform magnetic field B = B₀i + 2B₀j T… | JEE Main 2024 (31 Jan, Shift 1)

Q32JEE Main 2024 · 31 JAN · SHIFT 1Medium

Moving Charge in a Magnetic Field

An electron moves through a uniform magnetic field $\vec{B} = B_0\hat{i} + 2B_0\hat{j}\text{ T}$ . At a particular instant of time, the velocity of electron is $\vec{u} = 3\hat{i} + 5\hat{j}\text{ m/s}$ . If the magnetic force acting on electron is $\vec{F} = 5e\hat{k}\text{ N}$ , where $e$ is the charge of electron, then the value of $B_0$ is _________ $T$ .

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 5

$\vec F = -e(\vec u\times\vec B)$
$\vec u\times\vec B = (3\hat i + 5\hat j)\times(B_0\hat i + 2B_0\hat j) = (6B_0 - 5B_0)\hat k = B_0\hat k$
$-eB_0\hat k = 5e\hat k \Rightarrow B_0 = -5\text{ T}$
Magnitude of $B_0$ is $5\text{ T}$ .

Report a mistake

Moving Charge in a Magnetic Field question from JEE Main 2024 (31 Jan, Shift 1)

More questions on Moving Charge in a Magnetic Field