In a vacuum chamber, a particle of charge $1\ \mu C$ and mass $1\ \mathrm{mg}$ is projected with a velocity $(\hat{i} + 2\hat{j})\ \mathrm{ms}^{-1}$ from the $XZ$ plane at time $t = 0$ in an electric field of $1\hat{i}\ \mathrm{Vm}^{-1}$. At $t = 0.2\ s$, the electric field is switched off and a magnetic field of $6\hat{j}\ \mathrm{T}$ is switched on. The acceleration due to gravity is $-10\hat{j}\ \mathrm{ms}^{-2}$. Correct option(s) is/are :
A positive, singly ionized atom of mass number $A_{\mathrm{M}}$ is accelerated from rest by the voltage $192 \mathrm{~V}$. Thereafter, it enters a rectangular region of width $w$ with magnetic field $\vec{B}_0=0.1 \hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance $x$ below its starting trajectory.
[Given: Mass of neutron/proton $=(5 / 3) \times 10^{-27} \mathrm{~kg}$, charge of the electron $=1.6 \times 10^{-19} \mathrm{C}$.]
Which of the following option(s) is(are) correct?
A resistor R = 1.4 $$\Omega$$ and a capacitor C0 = 5.0$$\mu$$F are connected in series between the rails. At time t = 0, C0 is uncharged. Which of the following statement(s) is(are) correct? [$$\mu$$0 = 4$$\pi$$ $$\times$$ 10$$-$$7 SI units. Take ln 2 = 0.7]
JEE Advanced Subjects
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