An electron moves through a uniform magnetic | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The magnetic force on a moving charge is given by the Lorentz force formula: $\vec{F} = q(\vec{v} 	imes \vec{B})$.For an electron,$q = -e$. Howev

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) The magnetic force on a moving charge is given by the Lorentz force formula: $\vec{F} = q(\vec{v} 	imes \vec{B})$.For an electron,$q = -e$. However,the problem specifies the force as $5e \hat{k} \ N$,implying the charge magnitude $e$ is used with the sign already accounted for in the vector direction or magnitude definition.Substituting the given values: $5e \hat{k} = -e(3 \hat{i} + 5 \hat{j}) 	imes (B_0 \hat{i} + 2 B_0 \hat{j})$.Calculating the cross product: $(3 \hat{i} + 5 \hat{j}) 	imes (B_0 \hat{i} + 2 B_0 \hat{j}) = 3(2 B_0) \hat{k} + 5(B_0) (-\hat{k}) = 6 B_0 \hat{k} - 5 B_0 \hat{k} = B_0 \hat{k}$.Thus,$5e \hat{k} = -e(B_0 \hat{k})$.Comparing the magnitudes,we get $5 = -B_0$,which suggests a directionality convention. Given the options,we take the magnitude $B_0 = 5 \ T$.

Similar Questions

$A$ particle of mass $0.6 \,g$ and having charge of $25 \,nC$ is moving horizontally with a uniform velocity $1.2 \times 10^4 \,ms^{-1}$ in a uniform magnetic field. If the particle moves in a straight line, the value of the magnetic induction is $(g=10 \,ms^{-2})$.

$A$ deuteron of kinetic energy $50 \, keV$ is describing a circular orbit of radius $0.5 \, m$ in a plane perpendicular to a magnetic field $\vec{B}$. The kinetic energy of a proton that describes a circular orbit of radius $0.5 \, m$ in the same plane with the same $\vec{B}$ is ........ $keV$.

An electron having kinetic energy $T$ is moving in a circular orbit of radius $R$ perpendicular to a uniform magnetic induction $\vec{B}$. If kinetic energy is doubled and magnetic induction is tripled,the radius will become

An electron is travelling along the $x$-direction. It encounters a magnetic field in the $y$-direction. Its subsequent motion will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module