An electron accelerated through a potential difference $V$ enters a uniform transverse magnetic field and experiences a force $F$. If the accelerating potential is increased to $2V$, the electron in the same magnetic field will experience a force
A$F$
B$\frac{F}{2}$
C$\sqrt 2 F$
D$2F$
Medium
Download our app for free and get started
C$\sqrt 2 F$
c $F=B q v$
But $\frac{1}{2} m v^{2}=e V$ or $v=\sqrt{\frac{2 e V}{m}}$
$\therefore F=B q \sqrt{\frac{2e v}{m}}$
$\Rightarrow F \propto \sqrt{V}$ and
$F \propto \sqrt{2 V}$
$\frac{F^{\prime}}{F}=\sqrt{2}$ or $F^{\prime}=\sqrt{2} F$
Download our app
and 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.*
A square coil of side $10\; cm$ consists of $20$ turns and carries a current of $12\; A$. The coil is suspended vertically and the normal to the plane of the coil makes an angle of $30^o$ with the direction of a uniform horizontal magnetic field of magnitude $0.80 \;T$. What is the magnitude of torque (in $N\;m$) experienced by the coil?
An infinitely long conductor $PQR$ is bent to from a right angle as shown. A current $I$ flows through $PQR$ . The magnetic field due to this current at the point $M$ is $H_1$ . Now, another infinitely long straight conductor $QS$ is connected at $Q$ so that the current in $PQ$ remaining unchanged. The magnetic field at $M$ is now $H_2$ . The ratio $H_1/H_2$ is given by
The number of turns per unit length of a long solenoid is $10$ . If its average radius is $5 \,cm$ and it carries a current of $10 \,A$, then the ratio of flux densities obtained at the centre and at the end on the axis will be
A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is.......... and their speed is.................. in the ratio.
A particle of charge $q$ and mass $m$ moving with a velocity $v$ along the $x$-axis enters the region $x > 0$ with uniform magnetic field $B$ along the $\hat k$ direction. The particle will penetrate in this region in the $x$-direction upto a distance $d$ equal to
A proton carrying $1\, Me V$ kinetic energy is moving in a circular path of radius $R$ in uniform magnetic field. What should be the energy of an $\alpha -$ particle to describe a circle of same radius in the same field ?........$MeV$
One of the two small circular coils, (none of them having any self- inductance) is suspended with a $V-$ shaped copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both the coils are connected in series with a $dc$ supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect ?
A 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 be