10 Questions
What is the direction of the magnetic field created by a current element?
Perpendicular to both the length element dl and the unit vector r̂
What is the similarity between Biot-Savart law and Coulomb’s Law?
Both vary as the inverse square of the distance from the source
What is the direction of rotation of the thumb in Maxwell’s cork screw rule?
In the direction of rotation of the screw
What is the unit of the quantity dB in the Biot-Savart law?
Tesla
What is the physical quantity represented by the symbol q in Coulomb’s Law?
Electric charge
What is the expression for the magnetic field dB in the Biot-Savart law?
$\mu_0 idl \times \hat{r}$
What is the physical quantity represented by the symbol E in the diagram?
Electric field
What is the direction of the electric field created by a point charge?
Radial to the point charge
What is the constant of proportionality in Coulomb’s Law?
$1 / 4\pi\epsilon_0$
What is the physical quantity represented by the symbol B in the diagram?
Magnetic field
Study Notes
Biot-Savart Law
- Magnetic field at point 'P' due to a current element 'i dl' is given by the expression: dB = μ₀ i dl sin θ / 4π r²
- In C.G.S. units, k = 1, so dB = i dl sin θ / r² Gauss
- In S.I. units, k = μ₀ / 4π, so dB = μ₀ i dl sin θ / 4π r² Tesla
- μ₀ is the absolute permeability of air or vacuum, approximately 4π × 10⁻⁷
Magnetic Field and Current
- A magnetic field is established around a current-carrying conductor
- Magnetic field exists as long as there is current in the wire
- The direction of the magnetic field is reversed when the direction of current is reversed
Current Element
- Current element is the product of current and length of an infinitesimal segment of a current-carrying wire
- Current element is a vector quantity with the same direction as the current
- Current element AB = i dl
Biot-Savart's Law and Coulomb's Law
- Both laws relate to the inverse square of the distance from the source
- The current element produces a magnetic field, while a point charge produces an electric field
- The magnetic field created by a current element is perpendicular to both the length element dl and the unit vector r̂
Direction of Magnetic Field
- Determined using Maxwell's cork screw rule
- If a right-handed screw is placed along the current-carrying linear conductor and rotated in the direction of current flow, the direction of rotation of the thumb gives the direction of magnetic lines of force
This quiz is about the Biot-Savart Law, which relates to the magnetic field at a point due to a current element. It involves calculating the magnetic field using formulas.
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