Question
Distinguish between the forces experienced by a moving charge in a uniform electric field and in a uniform magnetic field.
✓
Answer
A charge q moving with a velocity $\vec{v}$ through a magnetic field of induction $\vec{B}$ experiences a magnetic force perpendicular both to $\vec{B}$ and $\vec{v}$. Experimental observations show that the magnitude of the force is proportional to the magnitude of $\vec{B}$, the speed of the particle, the charge $q$ and the sine of the angle $\theta$ between $\vec{v}$ and $\vec{B}$. That is, the magnetic force, $\mathrm{F}_{\mathrm{m}}=q v B \sin \theta$ $\therefore \vec{F}_{\mathrm{m}}=q(\vec{v} \times \vec{B})$
Therefore, at every instant $\vec{F}_{\mathrm{m}}$ acts in a direction perpendicular to the plane of $\vec{v}$ and $\vec{B}$
If the moving charge is negative, the direction of the force $\vec{F}_{\mathrm{m}}$ acting on it is opposite to that given by the right-handed screw rule for the cross-product $\vec{v} \times \vec{B}$
If the charged particle moves through a region of space where both electric and magnetic fields are present, both fields exert forces on the particle. The force due to the electric field $\vec{E}$ is $\vec{F}_{\mathrm{e}}=q \vec{E}$.
The total force on a moving charge in electric and magnetic fields is called the Lorentz force :
$
\vec{F}=\vec{F}_{\mathrm{e}}+\vec{F}_{\mathrm{m}}=q(\vec{E}+\vec{v} \times \vec{B})
$
Special cases :
(i) $\vec{v}$ is parallel or antiparallel to $\vec{B}$ : In this case, $\mathrm{F}_{\mathrm{m}}=\mathrm{qvB} \sin 0^{\circ}=0$. That is, the magnetic force on the charge is zero.
(ii) The charge is stationary $\{v=0)$ : In this case, even if $q \neq 0$ and $B \neq 0, F_m=$ $q(0) B \sin \theta=0$. That is, the magnetic force on a stationary charge is zero.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Explain gauge pressure and absolute pressure within a liquid open to the atmosphere.
OR
Explain the effect of gravity on fluid pressure.
OR
Explain the effect of gravity on fluid pressure.
Explain in brief the pressure difference across a curved liquid surface.
Potential energy of a particle performing linear S.H.M is $0.1 \pi ^2 x^2$ joule. If mass of the particle is $20\ g$, find the frequency of S.H.M.
→Find the capacity of a capacitor which when put in series with a $10 \Omega$ resistor makes the power factor equal to $0.5.$ Assume an $80\ V-100\ Hz\ AC$ supply.
→A ray of light is incident on a glass slab making an angle of $30^{\circ}$ with the surface. Calculate the angle of refraction in glass and the speed of light in glass. The refractive index of glass and speed of light in air are $1.5$ and $3 \times 10^8 m / s,$ respectively.
→A parallel beam of monochromatic light is incident on a glass slab at an angle of incidence $60^{\circ}$. Find the ratio of the width of the beam in glass to that in air if the refractive index of glass is $\frac{3}{2}$.
Data: $i =60, a n _g=1.5$
By Snell's law, ang $=\frac{\sin i}{\sin r} \therefore \sin r=\frac{\sin i}{\operatorname{sn} n_g}$
→Data: $i =60, a n _g=1.5$
By Snell's law, ang $=\frac{\sin i}{\sin r} \therefore \sin r=\frac{\sin i}{\operatorname{sn} n_g}$
Derive the relationship $\frac{V_{ P }}{V_{ S }}=\frac{I_{ S }}{I_{ P }}$ for a transformer.
→Explain the phenomenon of self induction and mutual induction. Define coefficient of self induction and mutual induction. Write the SI unit and dimensions of coefficient of self induction
The width of a plane incident wavefront is found to be doubled in a denser medium if it makes an angle of 70° with the surface. Calculate the refractive index for the denser medium.
The equation of linear SHM is a: $=10 \sin \left(4 \pi t+\frac{1}{24}\right) cm$. Find the amplitude, period and phase constant of the motion. Also, find the phase angle $\frac{1}{24}$ second after the start.
→