A long straight wire has fixed negative charge – In the realm of electrostatics, the study of a long straight wire with fixed negative charge unveils a fascinating interplay of electric fields and potentials. This wire, imbued with a negative charge, generates an electric field that permeates the surrounding space, shaping the behavior of nearby charges.
The electric field strength around the wire exhibits a radial dependence, decreasing inversely with the distance from the wire. This field exerts a force on charged particles, attracting positive charges and repelling negative charges. The electric potential, a scalar quantity, describes the work done in moving a unit charge from infinity to a given point in the field.
Electrostatic Field of a Long Straight Wire
The electrostatic field around a long straight wire with fixed negative charge is a radial field. The field lines are directed radially outward from the wire. The magnitude of the electric field at a distance rfrom the wire is given by:
$$E = \frac14\pi\varepsilon_0 \frac|\lambda|r$$
where:
- Eis the electric field strength
- λis the linear charge density of the wire
- ris the distance from the wire
- ε0is the permittivity of free space
Electric Potential Due to a Long Straight Wire
The electric potential at a point due to a long straight wire with fixed negative charge is given by:
$$V =
- \int_\infty^r \frac14\pi\varepsilon_0 \frac|\lambda|r’ dr’ =
- \frac14\pi\varepsilon_0 \frac|\lambda|r \ln\left(\fracrr_0\right)$$
where:
- Vis the electric potential
- λis the linear charge density of the wire
- ris the distance from the wire
- ε0is the permittivity of free space
- r0is a reference distance
Force on a Charge near a Long Straight Wire: A Long Straight Wire Has Fixed Negative Charge
The force experienced by a positive charge qplaced near a long straight wire with fixed negative charge is given by:
$$F = qE = \frac14\pi\varepsilon_0 \fracq|\lambda|r$$
where:
- Fis the force experienced by the charge
- qis the charge of the particle
- Eis the electric field strength
- λis the linear charge density of the wire
- ris the distance from the wire
- ε0is the permittivity of free space
The force experienced by a negative charge is in the opposite direction.
Applications of a Long Straight Wire with Fixed Negative Charge
Long straight wires with fixed negative charge have several practical applications, including:
- Particle accelerators:Long straight wires are used to accelerate charged particles in particle accelerators.
- Electron microscopes:Long straight wires are used to focus electron beams in electron microscopes.
Variations and Extensions
Variations of the problem of a long straight wire with fixed negative charge include:
- A long straight wire with positive charge
- A wire with varying charge distribution
Extensions to the problem include:
- The effect of a dielectric medium
- The presence of multiple wires
FAQ
What is the direction of the electric field around a long straight wire with fixed negative charge?
The electric field points radially outward from the wire.
How does the electric field strength vary with distance from the wire?
The electric field strength decreases inversely with the distance from the wire.
What is the force experienced by a positive charge placed near the wire?
A positive charge experiences an attractive force towards the wire.
