# Physics Questions and Answers – Magnetic Field due to a Current Element & Biot-Savart Law

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This set of Physics Problems for Schools focuses on “Magnetic Field due to a Current Element & Biot-Savart Law”.

1. Give the SI unit of magnetic permeability of free space.
a) T A m-2
b) T A-2 m
c) T A-1 m
d) T A m2

Explanation: Magnetic permeability of free space is a measure of the amount of resistance encountered when forming a magnetic field in a classical vacuum. The SI unit of permeability is weber ampere-1 metre-1 (Wb A-1 m-1) or tesla ampere-1meter (T A-1 m).

2. State the rule that is used to find the direction of field acting at a point near a current-carrying straight conductor.
a) Cork rule
b) The right-hand thumb rule
c) Swimming rule
d) Flemings rule

Explanation: Right-hand thumb rule can be used to find the direction of the magnetic field at a point near a current-carrying conductor. Right hand rule states that, if the thumb of the right hand is in the direction of the current flow then, the curl fingers show the direction of the magnetic field.

3. Give the dimensional formula for magnetic permeability of free space.
a) [M L T-2 A-2]
b) [M2 L T-2 A-2]
c) [M L2 T-2 A-2]
d) [M-1 L T-2 A-2]

Explanation: Magnetic permeability = Magnetic flux density × [Magnetic field strength]-1.
μ = [M L0 T-2 A-1] × [M0 L-1 T0 A1]-1
μ = [M L T-2 A-2].

4. A wire placed along the north-south direction carries a current of 8 A from south to north. Find the magnetic field due to a 1 cm piece of wire at a point 200 cm north-east from the piece.
a) 14 × 10-9 T
b) 1004 × 10-9 T
c) 204.4 × 10-9 T
d) 1.4 × 10-9 T

Explanation: dB = $$\frac {(\mu_0 I dl sin (\theta))}{(4\pi r^2)}$$.
dB = $$\frac {(4 \pi \, \times \, 10^{-7} \, \times \, 8 \, \times \, 1 \, \times \, 10^{-2} \, \times \, sin 45^o}{(4 \pi \, \times \, 22)}$$
dB = 1.4 × 10-9 T.

5. Which of the following is not a point of similarity between Biot-Savart law and Coulomb’s law.
a) Both fields depend inversely on the square of the distance from the source to the point of observation
b) They are not a universal law
c) The principle of superposition does not apply to both
d) Both are long-range fields

Explanation: The principle of superposition applies to both fields. This is because the magnetic field is linearly related to its source, namely, the current element and the electrostatic field is related linearly to its source, the electric charge.

6. The magnetic field due to a current element is minimum in a plane passing through the element when it is perpendicular to its axis. State true or false.
a) True
b) False

Explanation: If θ = 90o → sin θ = 1
→ Then dB is maximum.
The magnetic field due to a current element is maximum in a plane passing through the element and perpendicular to its axis.

7. Give the SI unit of the magnetic field from Biot-Savart law.
a) Ampere
b) Tesla
c) Weber
d) Gauss

Explanation: The SI unit of the magnetic field is the tesla (T). One tesla is 107 times the magnetic field produced by a conducting wire of length one meter and carrying a current of one ampere at a distance of one meter from it and perpendicular to it. 