In a certain region static electric and magnetic fields exist. The magnetic field is given by $\vec B = {B_0}\left( {\hat i + 2\hat j - 4\hat k} \right)$. If a test charge moving with a velocity $\vec v = {v_0}\left( {3\hat i - \hat j + 2\hat k} \right)$ experiences no force in that region, then the electric field in the region, in $SI\, units$, is
In a certain region static electric and magnetic fields exist. The magnetic field is given by $\vec B = {B_0}\left( {\hat i + 2\hat j - 4\hat k} \right)$. If a test charge moving with a velocity $\vec v = {v_0}\left( {3\hat i - \hat j + 2\hat k} \right)$ experiences no force in that region, then the electric field in the region, in $SI\, units$, is
- [JEE MAIN 2017]
- A
$\vec E = - {v_0}{B_0}\left( {3\hat i - 2\hat j - 4\hat k} \right)$
- B
$\vec E = - {v_0}{B_0}\left( {\hat i + \hat j + 7\hat k} \right)$
- C
$\vec E = {v_0}{B_0}\left( {14\hat j + 7\hat k} \right)$
- D
$\vec E = - {v_0}{B_0}\left( {14\hat j + 7\hat k} \right)$
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- [AIEEE 2012]
A positive, singly ionized atom of mass number $A_M$ is accelerated from rest by the voltage $192 V$. Thereafter, it enters a rectangular region of width $w$ with magnetic field $B_0=0.1 \hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance $x$ below its starting trajectory.
[Given: Mass of neutron/proton $=(5 / 3) \times 10^{-27} kg$, charge of the electron $=1.6 \times 10^{-19} C$.]
Which of the following option($s$) is(are) correct?
$(A)$ The value of $x$ for $H^{+}$ion is $4 cm$.
$(B)$ The value of $x$ for an ion with $A_M=144$ is $48 cm$.
$(C)$ For detecting ions with $1 \leq A_M \leq 196$, the minimum height $\left(x_1-x_0\right)$ of the detector is $55 cm$.
$(D)$ The minimum width $w$ of the region of the magnetic field for detecting ions with $A_M=196$ is $56 cm$.
A positive, singly ionized atom of mass number $A_M$ is accelerated from rest by the voltage $192 V$. Thereafter, it enters a rectangular region of width $w$ with magnetic field $B_0=0.1 \hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance $x$ below its starting trajectory.
[Given: Mass of neutron/proton $=(5 / 3) \times 10^{-27} kg$, charge of the electron $=1.6 \times 10^{-19} C$.]
Which of the following option($s$) is(are) correct?
$(A)$ The value of $x$ for $H^{+}$ion is $4 cm$.
$(B)$ The value of $x$ for an ion with $A_M=144$ is $48 cm$.
$(C)$ For detecting ions with $1 \leq A_M \leq 196$, the minimum height $\left(x_1-x_0\right)$ of the detector is $55 cm$.
$(D)$ The minimum width $w$ of the region of the magnetic field for detecting ions with $A_M=196$ is $56 cm$.
- [IIT 2024]