Given below are two statements: One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R).$
Assertion $(A)$ : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.
Reason $(R)$ : Moving charged particle experiences magnetic force perpendicular to its direction of motion.
Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $( A )$
Both $(A)$ and $(R)$ are true but $(R)$ is NOT the correct explanation of $( A )$
$(A)$ is true but $(R)$ is false
$(A)$ is false but $(R)$ is true.
A charged particle enters a uniform magnetic field with velocity vector making an angle of $30^o$ with the magnetic field. The particle describes a helical trajectory of pitch $x$ . The radius of the helix is
Answer the following questions:
$(a)$ A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
$(b)$ A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
$(c)$ An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.
Two parallel wires in the plane of the paper are distance $X _0$ apart. A point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have direction opposite to each other, the radius of curvature of the path is $R_2$.
If $\frac{x_0}{x_1}=3$, the value of $\frac{R_1}{R_2}$ is.
Two toroids $1$ and $2$ have total number of tums $200$ and $100 $ respectively with average radii $40\; \mathrm{cm}$ and $20 \;\mathrm{cm}$ respectively. If they carry same current $i,$ the ratio of the magnetic flelds along the two loops is
A proton and an alpha particle of the same enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the circular paths described by the alpha particle and proton is ....