An electron is moving at a speed of $3.2 \times 10^7 \ m/s$ in a magnetic field of $12 \times 10^{-4} \ T$ perpendicular to the direction of motion of the electron. The radius of the path of the electron is . . . . . . $cm$. $(e = 1.6 \times 10^{-19} \ C$ and $m_e = 9 \times 10^{-31} \ kg)$

$A$ charged particle is released from rest in a region of uniform electric and magnetic fields which are parallel to each other. The particle will move on a

An electron has mass $9 \times 10^{-31} \ kg$ and charge $1.6 \times 10^{-19} \ C$ is moving with a velocity of $10^6 \ m/s$. It enters a region where a magnetic field exists. If it describes a circle of radius $0.10 \ m$,the intensity of the magnetic field must be:

An electron is accelerated by a potential difference of $12000\, V$. It then enters a uniform magnetic field of $10^{-3}\, T$ applied perpendicular to the path of the electron. Find the radius of the path. Given: mass of electron $m = 9 \times 10^{-31}\, kg$ and charge on electron $q = 1.6 \times 10^{-19}\, C$.

In a parabola spectrograph,the velocities of four positive ions $P, Q, R,$ and $S$ are $v_1, v_2, v_3,$ and $v_4$ respectively. Based on the provided parabola spectrograph image,determine the relationship between their velocities.

Consider a long thin conducting wire carrying a uniform current $I$. $A$ particle having mass $M$ and charge $q$ is released at a distance $a$ from the wire with a speed $v_0$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance $x$ from the wire. The value of $x$ is [$\mu_0$ is vacuum permeability]