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 tripled, the radius will become
Medium
Download our app for free and get started
$r=\frac{m v}{q B}=\sqrt{\frac{2 m T}{q B}}$
$r^{\prime}=\frac{\sqrt{2 m(2 T)}}{q(3 B)}=\frac{\sqrt{2}}{3} r \Rightarrow \sqrt{\frac{2}{9}} R$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1$\alpha $ particle, proton and duetron enters in a uniform (transverse) magnetic field $'B'$ with same acceleration potential find ratio of radius of path followed by these particles.View Solution
- 2A wire $A$, bent in the shape of an arc of a circle, carrying a current of $2\, A$ and having radius $2\, cm$ and another wire $B ,$ also bent in the shape of arc of a circle, carrying a current of $3\, A$ and having radius of $4\, cm ,$ are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre $O$ isView Solution
- 3A wire carrying current $I$ has the shape as shown in adjoining figure.Linear parts of the wire are very long and parallel to $X-$axis while semicircular portion of radius $R$ is lying in $Y-Z$ plane. Magnetic field at point $O$ isView Solution
- 4In hydrogen atom, an electron is revolving in the orbit of radius $0.53\,{\mathop A\limits^o }$ with $6.6 \times {10^{15}}$ $rotations/second$. Magnetic field produced at the centre of the orbit is.......$wb/{m^2}$View Solution
- 5Given below are two statement :View Solution
Statement $I :$ If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.
Statement $II :$ Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio:
In the light of the above statement, choose the correct answer from the options given below :
- 6A long straight wire of circular cross-section (radius $a$) is carrying steady current $I$. The current $I$ is uniformly distributed across this cross-section. The magnetic field isView Solution
- 7Consider the inferences given below in respect of the following current loop of wire kept is a magnetic field $\vec B$View Solution
$A.$ The force on the element $AC$ of the wire is $\frac{{\sqrt 3 }}{2}\,ILB$ directed into the page
$B.$ The force on the element $AB$ of the wire is $\frac{{\sqrt 3 }}{2}\,ILB$ directed into the page
$C.$ The total force on the loop $ABCA$ is zero.
Which of the above is /are not true ?
- 8Two parallel conductors $A$ and $B$ of equal lengths carry currents $I$ and $10\, I$, respectively, in the same direction. ThenView Solution
- 9A particle with charge $-Q$ and mass m enters a magnetic field of magnitude $B,$ existing only to the right of the boundary $YZ$. The direction of the motion of the $m$ particle is perpendicular to the direction of $B.$ Let $T = 2\pi\frac{m}{{QB}}$ . The time spent by the particle in the field will beView Solution
- 10View SolutionBohr magneton is given by (symbols have their usual meanings)