Biot–Savart law and magnetic field of current elements - One Line Questions
1.
What is the magnetic field at the center of a current-carrying loop shaped like a regular n-gon? —
(nμ₀I / 2a) * cot(π/n)
2.
For a finite straight wire of length L, the magnetic field at the end of the wire on the perpendicular bisector at distance r is: —
(μ₀I / 4πr) * (1 / sqrt(1 + (L/2r)²))
3.
The magnetic field produced by a finite straight wire of length L carrying current I at a point on its perpendicular bisector at a distance r from the midpoint is: —
(μ₀I / 4πr) * (L / sqrt(r² + (L/2)²))
4.
The magnetic field on the axis of a circular loop of radius R carrying current I at a distance x from the center is: —
(μ₀IR²) / (2(R² + x²)^(3/2))
5.
What is the magnetic field at a point on the axis of a finite solenoid of length L and radius R, with n turns per unit length, carrying current I? —
(μ₀nI / 2) * (cosθ₁ - cosθ₂)
6.
The magnetic field at the center of a current-carrying hexagon of side 'a' is: —
3√3 μ₀I / (2πa)
7.
The magnetic field produced by a current element is strongest when the angle between the current element vector and the position vector is: —
90 degrees
8.
The magnetic field at a point P due to a current element Idl is zero when the angle between Idl and r is: —
0 degrees or 180 degrees
9.
For an infinitely long solenoid, the angles θ₁ and θ₂ in the formula (μ₀nI / 2) * (cosθ₁ - cosθ₂) approach: —
0° and 90° respectively
10.
The magnetic field at a large distance x from the center of a circular loop of radius R carrying current I is proportional to: —
1/x³
11.
The magnetic field at the center of a current-carrying square loop of side length 'a' is: —
2μ₀I / (πa)
12.
The magnetic field at the center of a current-carrying equilateral triangle of side 'a' is: —
3μ₀I / (2πa)
13.
What is the value of μ₀? —
4π × 10⁻⁷ T m/A
14.
Consider a current element Idl. The magnetic field dB at a distance r is zero when the point is located: —
Along the line containing the current element
15.
What is the direction of the magnetic field around a long straight wire carrying current, according to the right-hand rule? —
In concentric circles around the wire, perpendicular to the wire
16.
The Biot-Savart law is a consequence of which fundamental principle? —
Superposition principle
17.
If a current element is a loop, the Biot-Savart law is used to calculate the field by integrating over the entire loop: —
dB = (μ₀ / 4π) * (Idl x r) / r³
18.
What is the Biot-Savart law used to calculate? —
Magnetic field due to a current element
19.
The Biot-Savart law is a fundamental law for calculating: —
Magnetic field generated by steady currents
20.
The Biot-Savart law is analogous to which law in electrostatics? —
Coulomb's Law
21.
The Biot-Savart law is derived from: —
Ampere's Circuital Law
22.
If the current in a wire is doubled, the magnetic field produced by it will: —
Double
23.
If the distance from a current element is doubled, the magnetic field produced by it will: —
Become one-fourth
24.
The Biot-Savart law states that the magnetic field dB produced by a current element Idl is proportional to: —
Idl sin(theta) / r^2
25.
Which statement about the Biot-Savart law is incorrect? —
The magnetic field is directly proportional to the sine of the angle between the current element and the position vector.
26.
What is the direction of the magnetic field dB due to a current element Idl at a point P? —
Perpendicular to both Idl and the position vector r
27.
The magnetic field at a point P due to a current element Idl is given by dB. If the current is reversed, the magnetic field dB will: —
Reverse its direction
28.
The Biot-Savart law is applicable for: —
Steady currents only
29.
The Biot-Savart law is particularly useful for calculating magnetic fields from: —
Asymmetrical current distributions
30.
The unit of magnetic field is: —
Tesla (T)
31.
For a circular loop, the magnetic field on the axis is maximum at: —
The center of the loop (x=0)
32.
The magnetic field at the center of a current-carrying loop is proportional to: —
The diameter of the loop
33.
Which of the following quantities is NOT required to determine the magnetic field at a point using the Biot-Savart law? —
The mass of the charge carriers
34.
The magnetic field at the center of a current-carrying wire bent into a circle of radius R is independent of: —
The shape of the wire
35.
In the formula dB = (μ₀ / 4π) * (Idl sinθ / r²), the term Idl represents: —
The product of current and infinitesimal length vector
36.
In the Biot-Savart law, what does 'r' represent? —
The distance from the current element to the point where the field is measured
37.
The magnetic field at a point on the axis of a circular loop is along: —
The axis of the loop
38.
The direction of the magnetic field dB due to a current element Idl is determined by: —
The right-hand rule
39.
The magnetic field inside a long solenoid is: —
Uniform and parallel to the axis
40.
Which vector quantity is represented by the term Idl in the Biot-Savart law? —
Current element vector
41.
For a current element Idl, when is the magnetic field dB maximum at a distance r? —
When θ = 90°
42.
For a current element Idl, when is the magnetic field dB zero at a distance r? —
When θ = 0° or θ = 180°
43.
The constant of proportionality in the Biot-Savart law in vacuum is: —
μ₀ / 4π
44.
The magnetic field due to a long straight wire carrying current I at a perpendicular distance r from the wire is given by: —
μ₀I / (2πr)
45.
The magnetic field at the center of a circular loop of radius R carrying current I is: —
μ₀I / (2R)
46.
The magnetic field at the center of a semicircle of radius R carrying current I is: —
μ₀I / (4R)
47.
What is the magnetic field at the center of an infinite solenoid carrying current I with n turns per unit length? —
μ₀nI
48.
The magnetic field outside a long solenoid is approximately: —
Zero
49.
The magnetic field at the center of a current-carrying toroid is: —
μ₀NI / (2πr)