The electric field in a region is given
$\overrightarrow{\mathrm{E}}=\left(\frac{3}{5} \mathrm{E}_{0} \hat{\mathrm{i}}+\frac{4}{5} \mathrm{E}_{0} \hat{\mathrm{j}}\right) \frac{\mathrm{N}}{\mathrm{C}}$. The ratio of flux of
reported field through the rectangular surface of area $0.2 \mathrm{~m}^{2}$ (parallel to $\mathrm{y}-\mathrm{z}$ plane) to that of the surface of area $0.3 \mathrm{~m}^{2}$ (parallel to $x-z$ plane) is $a: b$, where $a=$_________.
[Here $\hat{\mathrm{i}}, \hat{\mathrm{j}}$ and $\hat{\mathrm{k}}$ are unit vectors along $x, y$ and z-axes respectively]
$\overrightarrow{\mathrm{E}}=\left(\frac{3 \mathrm{E}_{0}}{5} \hat{\mathrm{i}}+\frac{4 \mathrm{E}_{0}}{5} \hat{\mathrm{j}}\right) \frac{N}{\mathrm{C}}$
$\mathrm{A}_{1}=0.2 \mathrm{~m}^{2}$ [parallel to $\mathrm{y}-\mathrm{z}$ plane]
$=\overrightarrow{\mathrm{A}}_{1}=0.2 \mathrm{~m}^{2} \hat{\mathrm{i}}$
$\mathrm{A}_{2}=0.3 \mathrm{~m}^{2}$ [parallel to $\mathrm{x}-\mathrm{z}$ plane]
$\overrightarrow{\mathrm{A}}_{2}=0.3 \mathrm{~m}^{2} \hat{\mathrm{j}}$
Now $\phi_{\mathrm{a}}=\left[\frac{3 \mathrm{E}_{0}}{5} \hat{\mathrm{i}}+\frac{4 \mathrm{E}_{0}}{5} \hat{\mathrm{j}}\right] \cdot[0.2 \hat{\mathrm{i}}]=\frac{3 \times 0.2}{5} \mathrm{E}_{0}$
$\& \quad \phi_{\mathrm{b}}=\left[\frac{3 \mathrm{E}_{0}}{5} \hat{\mathrm{i}}+\frac{4 \mathrm{E}_{0}}{5} \hat{\mathrm{j}}\right] \cdot[0.3 \hat{\mathrm{j}}]=\frac{4 \times 0.3}{5} \mathrm{E}_{0}$
Now $\frac{\phi_{\mathrm{a}}}{\phi_{\mathrm{b}}}=\frac{0.6}{1.2}=\frac{1}{2}=\frac{\mathrm{a}}{\mathrm{b}}$
$\Rightarrow a: b=1: 2$
$\Rightarrow a=1$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,