Alternating Current and Electromagnetic Waves
A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity $\overrightarrow{\mathrm{v}}$. A uniform electric field $\overrightarrow{\mathrm{E}}$ and a uniform magnetic field $\overrightarrow{\mathrm{B}}$ exist everywhere. The velocity $\overrightarrow{\mathrm{v}}$ , electric field $\overrightarrow{\mathrm{E}}$ and magnetic field $\overrightarrow{\mathrm{B}}$ are given in column 1, 2 and 3, respectively. The quantities E_{0}, B_{0} are positive in magnitude. |
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Column-1 | Column-2 | Column-3 |
(I) Electron with $\overrightarrow{\mathrm{v}}=2\frac{{\mathrm{E}}_{0}}{{\mathrm{B}}_{0}}\hat{\mathrm{x}}$ | (i) $\overrightarrow{\mathrm{E}}={\mathrm{E}}_{0}\hat{\mathrm{z}}$ | (P) $\overrightarrow{\mathrm{B}}=-{\mathrm{B}}_{0}\hat{\mathrm{x}}$ |
(II) Electron with $\overrightarrow{\mathrm{v}}=\frac{{\mathrm{E}}_{0}}{{\mathrm{B}}_{0}}\hat{\mathrm{y}}$ | (ii) $\overrightarrow{\mathrm{E}}=-{\mathrm{E}}_{0}\hat{\mathrm{y}}$ | (Q) $\overrightarrow{\mathrm{B}}={\mathrm{B}}_{0}\hat{\mathrm{x}}$ |
(III) Proton with $\overrightarrow{\mathrm{v}}=0$ | (iii) $\overrightarrow{\mathrm{E}}=-{\mathrm{E}}_{0}\hat{\mathrm{x}}$ | (R) $\overrightarrow{\mathrm{B}}={\mathrm{B}}_{0}\hat{\mathrm{y}}$ |
(IV) Proton with $\overrightarrow{\mathrm{v}}=2\frac{{\mathrm{E}}_{0}}{{\mathrm{B}}_{0}}\hat{\mathrm{x}}$ | (iv) $\overrightarrow{\mathrm{E}}={\mathrm{E}}_{0}\hat{\mathrm{x}}$ | (S) $\overrightarrow{\mathrm{B}}={\mathrm{B}}_{0}\hat{\mathrm{z}}$ |
In which case will the particle move in a straight line with constant velocity ?
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JEE Advanced 2017
Match List-I (electromagnetic wave type) with List-II (its association/application) and select the correct option from the choices given below.
List-I | List-II | ||
(a) | Infrared waves | (i) | To treat muscular strain |
(b) | Radio waves | (ii) | For broadcasting |
(c) | X-rays | (iii) | To detect fracture of bones |
(d) | Ultraviolet rays | (iv) | Absorbed by the ozone layer of the atmosphere |
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JEE Mains 2014
A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity $\overrightarrow{v}$. A uniform electric field $\overrightarrow{\mathrm{E}}$ and a uniform magnetic field $\overrightarrow{\mathit{B}}$ exists everywhere. The velocity $\overrightarrow{v}$, electric field $\overrightarrow{\mathrm{E}}$ and magnetic field $\overrightarrow{\mathit{B}}$ are given in columns 1, 2 and 3 respectively. The quantities E_{0}, B_{0} are positive is magnitude.
In which case will the particle move in a straight line with constant velocity?
Column 1 | Column 2 | Column 3 | |||
(I) | electron with $\overline{v}=\frac{3{E}_{0}}{{B}_{0}}\hat{x}$ | (i) | $\overrightarrow{E}=-9{E}_{0}\hat{x}$ | (P) | $\overrightarrow{B}=3{B}_{0}\hat{z}$ |
(II) | electron with $\overline{v}=\frac{3{E}_{0}}{{B}_{0}}\hat{y}$ | (ii) | $\overrightarrow{E}=3{E}_{0}\hat{z}$ | (Q) | $\overrightarrow{B}={B}_{0}\hat{z}$ |
(III) | Proton with $\overline{v}=0$ | (iii) | $\overrightarrow{E}=-{E}_{0}\hat{x}$ | (R) | $\overrightarrow{B}=2{B}_{0}\hat{y}$ |
(IV) | Proton with $\overline{v}=\frac{5{E}_{0}}{{B}_{0}}\hat{x}$ | (iv) | $\overrightarrow{E}=-{E}_{0}\hat{y}$ | (S) | $\overrightarrow{B}=-{B}_{0}\hat{x}$ |
In which case will the particle move in a straight line with constant velocity?
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JEE Advanced 0
A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity $\overrightarrow{v}$. A uniform electric field $\overrightarrow{\mathrm{E}}$ and a uniform magnetic field $\overrightarrow{\mathit{B}}$ exists everywhere. The velocity $\overrightarrow{v}$, electric field $\overrightarrow{\mathrm{E}}$ and magnetic field $\overrightarrow{\mathit{B}}$ are given in columns 1, 2 and 3 respectively. The quantities E_{0}, B_{0} are positive is magnitude.
In which case will the particle describe a helical path with the axis along the positive z-direction?
Column 1 | Column 2 | Column 3 | |||
(I) | electron with $\overline{v}=\frac{3{E}_{0}}{{B}_{0}}\hat{x}$ | (i) | $\overrightarrow{E}=-9{E}_{0}\hat{x}$ | (P) | $\overrightarrow{B}=3{B}_{0}\hat{z}$ |
(II) | electron with $\overline{v}=\frac{3{E}_{0}}{{B}_{0}}\hat{y}$ | (ii) | $\overrightarrow{E}=3{E}_{0}\hat{z}$ | (Q) | $\overrightarrow{B}={B}_{0}\hat{z}$ |
(III) | Proton with $\overline{v}=0$ | (iii) | $\overrightarrow{E}=-{E}_{0}\hat{x}$ | (R) | $\overrightarrow{B}=2{B}_{0}\hat{y}$ |
(IV) | Proton with $\overline{v}=\frac{5{E}_{0}}{{B}_{0}}\hat{x}$ | (iv) | $\overrightarrow{E}=-{E}_{0}\hat{y}$ | (S) | $\overrightarrow{B}=-{B}_{0}\hat{x}$ |
In which case will the particle describe a helical path with the axis along the positive z-direction?
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JEE Advanced 0
A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity $\overrightarrow{v}$. A uniform electric field $\overrightarrow{\mathrm{E}}$ and a uniform magnetic field $\overrightarrow{\mathit{B}}$ exists everywhere. The velocity $\overrightarrow{v}$, electric field $\overrightarrow{\mathrm{E}}$ and magnetic field $\overrightarrow{\mathit{B}}$ are given in columns 1, 2 and 3 respectively. The quantities E_{0}, B_{0} are positive is magnitude.
In which case would the particle move in a straight line along the negative direction of y-axis (i.e. move along $-\hat{y}$)?
Column 1 | Column 2 | Column 3 | |||
(I) | Electron with $\overline{v}=\frac{3{E}_{0}}{{B}_{0}}\hat{x}$ | (i) | $\overrightarrow{E}=-9{E}_{0}\hat{x}$ | (P) | $\overrightarrow{B}=3{B}_{0}\hat{z}$ |
(II) | Electron with $\overline{v}=\frac{3{E}_{0}}{{B}_{0}}\hat{y}$ | (ii) | $\overrightarrow{E}=3{E}_{0}\hat{z}$ | (Q) | $\overrightarrow{B}={B}_{0}\hat{z}$ |
(III) | Proton with $\overline{v}=0$ | (iii) | $\overrightarrow{E}=-{E}_{0}\hat{x}$ | (R) | $\overrightarrow{B}=2{B}_{0}\hat{y}$ |
(IV) | Proton with $\overline{v}=\frac{5{E}_{0}}{{B}_{0}}\hat{x}$ | (iv) | $\overrightarrow{E}=-{E}_{0}\hat{y}$ | (S) | $\overrightarrow{B}=-{B}_{0}\hat{x}$ |
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JEE Advanced 0
In the circuit shown in figure
E = 20 V, L = 5 H, C = 10 μF, R_{1} = 1 Ω , R_{2} = 2 Ω , R_{3} = 3 Ω switch S is closed at t = 0
E = 20 V, L = 5 H, C = 10 μF, R_{1} = 1 Ω , R_{2} = 2 Ω , R_{3} = 3 Ω switch S is closed at t = 0
Column-I | Column-II | ||
A | Current through R_{3} at t = 0 | P | 0 A |
B | Current through R_{3 }at t = ∞ | Q | 2 A |
C | Current through R_{1 }at t = 0 | R | 4 A |
D | Current through R_{2} at t = ∞ | S | 5 A |
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JEE Advanced 0
Time constants of the given circuits in column I are in column II. Match the respective values and choose the correct option.
Column I | Column II | ||
(P) | (1) | RC | |
(Q) | (2) | 2RC | |
(R) | (3) | $\frac{RC}{2}$ | |
(S) | (4) | $\frac{3RC}{2}$ |
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JEE Advanced 0