10 Questions
Match the following forms of Biot-Savart's law with their respective expressions:
Vector form = $\frac{\mu i}{4\pi r^2} dl \times r^\hat$ In terms of current density = $\frac{\mu J}{4\pi r^2} \times r^\hat$ In terms of charge and its velocity = $\frac{\mu qv \times r^\hat}{4\pi r^3}$ Scalar form = $\frac{\mu i dl}{4\pi r^2}$
Match the following directions with their respective descriptions:
Perpendicular to both dL and r^\hat = Direction of dB Parallel to dL = Direction of current flow Parallel to r^\hat = Direction of position vector Parallel to J = Direction of current density
Match the following units with their respective quantities:
Ampere-metre = Magnetic moment Tesla-metre = Magnetic field strength Henry = Inductance Ampere = Current
Match the following expressions with their respective physical quantities:
idL = Current element qv = Charge velocity J = Current density dl = Infinitesimal length
Match the following formulas with their respective applications:
dB = (\mu i / 4\pi r^2) dl \times r^\hat = Calculation of magnetic field due to a current element dB = (\mu J / 4\pi r^2) \times r^\hat = Calculation of magnetic field due to a current density dB = (\mu qv \times r^\hat / 4\pi r^3) = Calculation of magnetic field due to a moving charge dB = (\mu i / 4\pi r^2) dl = Calculation of magnetic field due to a current
Match the following quantities with their respective units:
Magnetic field strength = Tesla Magnetic moment = Ampere-metre Inductance = Henry Current density = Ampere per metre squared
Match the following symbols with their respective meanings:
dl = Infinitesimal length r^\hat = Unit vector in the direction of position vector i = Current J = Current density
Match the following expressions with their respective physical quantities:
qv = Charge velocity idL = Current element J = Current density dl = Infinitesimal length
Match the following formulas with their respective applications:
dB = (\mu i / 4\pi r^2) dl = Calculation of magnetic field due to a current dB = (\mu J / 4\pi r^2) \times r^\hat = Calculation of magnetic field due to a current density dB = (\mu qv \times r^\hat / 4\pi r^3) = Calculation of magnetic field due to a moving charge dB = (\mu i / 4\pi r^2) dl \times r^\hat = Calculation of magnetic field due to a current element
Match the following physical quantities with their respective descriptions:
Current density = Current per unit area Current element = Infinitesimal current carrying length Magnetic field strength = Force per unit current per unit length Magnetic moment = Measure of the strength of a magnet
Study Notes
Magnetic Effect of Current
- A magnetic field is established around a current-carrying conductor, as discovered by Oersted.
- The magnetic field exists as long as there is current in the wire, and the direction of the magnetic field changes when the direction of the current is reversed.
- A moving charge produces both magnetic and electric fields, whereas a stationary charge only produces an electric field.
Biot-Savart's Law
- Biot-Savart's law is used to determine the magnetic field at any point due to a current-carrying conductor.
- The law is applicable for infinitesimally small conductors, but can be used for long conductors as well.
- The current element is the product of current and length of an infinitesimal segment of the current-carrying wire.
- The current element is a vector quantity, with its direction being the same as the direction of the current.
Current Element
- The current element is represented by the equation:
id l - The direction of the current element is the same as the direction of the current.
Biot-Savart Law Equation
- The Biot-Savart law equation is:
dB = (μ0 id l x rˆ) / 4π r^2 - The equation is similar to Coulomb's Law, with the magnetic field varying as the inverse square of the distance from the current element.
Similarities and Differences with Coulomb's Law
- Both laws have the same form, with the magnetic field and electric field varying as the inverse square of the distance.
- The magnetic field created by a current element is perpendicular to both the length element
d land the unit vectorrˆ, whereas the electric field created by a point charge is radial.
Direction of Magnetic Field
- The direction of the magnetic field is determined using Maxwell's cork screw rule.
- The rule states that if a right-handed screw is placed along the current-carrying linear conductor and rotated in the direction of the flow of current, the direction of rotation of the thumb gives the direction of the magnetic lines of force.
Units of Magnetic Field
- The units of magnetic field are
TeslaorAmp/metre. - Other units of magnetic field are
HenryorAmpere.
Different Forms of Biot-Savart's Law
- The vector form of Biot-Savart's law is:
dB = (μ i dl x rˆ) / 4π r^2 - The law can also be expressed in terms of current density:
dB = (μ J x rˆ) / 4π r^3 - The law can also be expressed in terms of charge and its velocity:
dB = (μ q v x rˆ) / 4π r^3
Learn about the magnetic field established around a current-carrying conductor, including Oersted's discovery and the concept of magnetic lines of force.
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