Two long parallel conductors $S_{1}$ and $S_{2}$ are separated by a distance $10 \,cm$ and carrying currents of $4\, A$ and $2 \,A$ respectively. The conductors are placed along $x$-axis in $X - Y$ plane. There is a point $P$ located between the conductors (as shown in figure).
A charge particle of $3 \pi$ coulomb is passing through the point $P$ with velocity
$\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s$; where $\hat{i}$ and $\hat{j} \quad$ represents unit vector along $x$ and $y$ axis respectively.
The force acting on the charge particle is $4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N$. The value of $x$ is
Two long parallel conductors $S_{1}$ and $S_{2}$ are separated by a distance $10 \,cm$ and carrying currents of $4\, A$ and $2 \,A$ respectively. The conductors are placed along $x$-axis in $X - Y$ plane. There is a point $P$ located between the conductors (as shown in figure).
A charge particle of $3 \pi$ coulomb is passing through the point $P$ with velocity
$\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s$; where $\hat{i}$ and $\hat{j} \quad$ represents unit vector along $x$ and $y$ axis respectively.
The force acting on the charge particle is $4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N$. The value of $x$ is
- [JEE MAIN 2022]
- A
$2$
- B
$1$
- C
$3$
- D
$-3$
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In the product
$\overrightarrow{\mathrm{F}} =\mathrm{q}(\vec{v} \times \overrightarrow{\mathrm{B}})$
$=\mathrm{q} \vec{v} \times\left(\mathrm{B} \hat{i}+\mathrm{B} \hat{j}+\mathrm{B}_{0} \hat{k}\right)$
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$\overrightarrow{\mathrm{F}} =\mathrm{q}(\vec{v} \times \overrightarrow{\mathrm{B}})$
$=\mathrm{q} \vec{v} \times\left(\mathrm{B} \hat{i}+\mathrm{B} \hat{j}+\mathrm{B}_{0} \hat{k}\right)$
For $\mathrm{q}=1$ and $\vec{v}=2 \hat{i}+4 \hat{j}+6 \hat{k}$ and
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What will be the complete expression for $\vec{B}$ ?
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In a chamber, a uniform magnetic field of $6.5 \;G \left(1 \;G =10^{-4} \;T \right)$ is maintained. An electron is shot into the field with a speed of $4.8 \times 10^{6} \;m s ^{-1}$ normal to the field.the radius of the circular orbit of the electron is $4.2 \;cm$. obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.
$\left(e=1.5 \times 10^{-19} \;C , m_{e}=9.1 \times 10^{-31}\; kg \right)$
In a chamber, a uniform magnetic field of $6.5 \;G \left(1 \;G =10^{-4} \;T \right)$ is maintained. An electron is shot into the field with a speed of $4.8 \times 10^{6} \;m s ^{-1}$ normal to the field.the radius of the circular orbit of the electron is $4.2 \;cm$. obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.
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