A particle having a mass of $10^{- 2} \,kg$ carries a charge of $5 \times 10^{-8}\, C.$ The particle is given an initial horizontal velocity of $10^5\, m/s $ in the presence of electric field $E$ and magnetic field $B.$ To keep the particle moving in a horizontal direction, it is necessary that
$(1)$ $\vec B$ should be perpendicular to the direction of velocity and $\vec E$ should be along the direction of velocity
$(2)$ Both $\vec B$ and $\vec E$ should be along the direction of velocity
$(3)$ Both $\vec B$ and $\vec E$ are mutually perpendicular and perpendicular to the direction of velocity.
$(4)$ $\vec B$ should be along the direction of velocity and $\vec E$ should be perpendicular to the direction of velocity
Which one of the following pairs of statements is possible?
A particle having a mass of $10^{- 2} \,kg$ carries a charge of $5 \times 10^{-8}\, C.$ The particle is given an initial horizontal velocity of $10^5\, m/s $ in the presence of electric field $E$ and magnetic field $B.$ To keep the particle moving in a horizontal direction, it is necessary that
$(1)$ $\vec B$ should be perpendicular to the direction of velocity and $\vec E$ should be along the direction of velocity
$(2)$ Both $\vec B$ and $\vec E$ should be along the direction of velocity
$(3)$ Both $\vec B$ and $\vec E$ are mutually perpendicular and perpendicular to the direction of velocity.
$(4)$ $\vec B$ should be along the direction of velocity and $\vec E$ should be perpendicular to the direction of velocity
Which one of the following pairs of statements is possible?
- [AIPMT 2010]
- A
$1$ and $ 3$
- B
$3 $ and $ 4$
- C
$2 $ and $ 3$
- D
$2$ and $4$
Similar Questions
In the product
$\overrightarrow{\mathrm{F}} =\mathrm{q}(\vec{v} \times \overrightarrow{\mathrm{B}})$
$=\mathrm{q} \vec{v} \times\left(\mathrm{B} \hat{i}+\mathrm{B} \hat{j}+\mathrm{B}_{0} \hat{k}\right)$
For $\mathrm{q}=1$ and $\vec{v}=2 \hat{i}+4 \hat{j}+6 \hat{k}$ and
$\overrightarrow{\mathrm{F}}=4 \hat{i}-20 \hat{j}+12 \hat{k}$
What will be the complete expression for $\vec{B}$ ?
In the product
$\overrightarrow{\mathrm{F}} =\mathrm{q}(\vec{v} \times \overrightarrow{\mathrm{B}})$
$=\mathrm{q} \vec{v} \times\left(\mathrm{B} \hat{i}+\mathrm{B} \hat{j}+\mathrm{B}_{0} \hat{k}\right)$
For $\mathrm{q}=1$ and $\vec{v}=2 \hat{i}+4 \hat{j}+6 \hat{k}$ and
$\overrightarrow{\mathrm{F}}=4 \hat{i}-20 \hat{j}+12 \hat{k}$
What will be the complete expression for $\vec{B}$ ?
- [NEET 2021]
If the magnetic field is parallel to the positive $y-$axis and the charged particle is moving along the positive $x-$axis (Figure), which way would the Lorentz force be for
$(a)$ an electron (negative charge),
$(b)$ a proton (positive charge).
If the magnetic field is parallel to the positive $y-$axis and the charged particle is moving along the positive $x-$axis (Figure), which way would the Lorentz force be for
$(a)$ an electron (negative charge),
$(b)$ a proton (positive charge).
An electron and a positron are released from $(0, 0, 0)$ and $(0, 0, 1.5\, R)$ respectively, in a uniform magnetic field ${\rm{\vec B = }}{{\rm{B}}_0}{\rm{\hat i}}$ , each with an equal momentum of magnitude $P = eBR$. Under what conditions on the direction of momentum will the orbits be non-intersecting circles ?
An electron and a positron are released from $(0, 0, 0)$ and $(0, 0, 1.5\, R)$ respectively, in a uniform magnetic field ${\rm{\vec B = }}{{\rm{B}}_0}{\rm{\hat i}}$ , each with an equal momentum of magnitude $P = eBR$. Under what conditions on the direction of momentum will the orbits be non-intersecting circles ?
A stream of charged particles enter into a region with crossed electric and magnetic fields as shown in the figure below. On the other side is a screen with a hole that is right on the original path of the particles. Then,
A stream of charged particles enter into a region with crossed electric and magnetic fields as shown in the figure below. On the other side is a screen with a hole that is right on the original path of the particles. Then,
- [KVPY 2009]
Answer the following questions:
$(a)$ A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
$(b)$ A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
$(c)$ An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.
Answer the following questions:
$(a)$ A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
$(b)$ A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
$(c)$ An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.