An electric dipole is placed on $x$-axis in proximity to a line charge of linear charge density $3.0 \times 10^{-6} \mathrm{C} / \mathrm{m}$. Line charge is placed on $\mathrm{z}$-axis and positive and negative charge of dipole is at a distance of $10 \mathrm{~mm}$ and $12 \mathrm{~mm}$ from the origin respectively. If total force of $4 \mathrm{~N}$ is exerted on the dipole, find out the amount of positive or negative charge of the dipole.
$815.1 \mathrm{nC}$
$8.8 \mu \mathrm{C}$
$0.485 \mathrm{mC}$
$4.44 \mu \mathrm{C}$
Correct Option: , 4
$\mathrm{r}=10 \mathrm{~mm}, \mathrm{x}=2$
$\left|\overrightarrow{\mathrm{F}}_{\mathrm{q}}\right|=\frac{2 \mathrm{k} \lambda}{\mathrm{r}} \cdot \mathrm{q}$
$\left|\overrightarrow{\mathrm{F}}_{-\mathrm{q}}\right|=\frac{2 \mathrm{k} \lambda}{\mathrm{r}+\mathrm{x}} \cdot \mathrm{q}$
$\Rightarrow \quad\left|\vec{F}_{\text {net }}\right|=\frac{2 k \lambda q}{r}-\frac{2 k \lambda q}{r+x}$
$\left|\vec{F}_{\text {net }}\right|=\frac{2 k \lambda q \cdot x}{r(r+x)}$
$4=\frac{2 \times 9 \times 10^{9} \times 3 \times 10^{-6} \times \mathrm{q} \times 2 \mathrm{~mm}}{10 \mathrm{~mm} .12 \mathrm{~mm}}$
$\Rightarrow \quad q=4.44 \mu C$
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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,