Q. 15.0( 1 Vote )

# A magnetic field

Answer :

Explanation: A magnetic current can be produced by a moving

charge. If the charge is moving uniformly, it will generate a constant

current. If we assume a constant current is flowing through a

conductor of length L, the magnetic field due to it at a distance R

from it is given by Biot-Savart law. The field would be

where i is the constant current and μ_{0} is the magnetic permeability

of free space and its value is 4π × 10^{-7} T m A^{-1}. So A. is correct.

A changing electric field can also generate a magnetic field around it. According to Ampere-Maxwell law, the total magnetic field around a region is due to flow of charge carriers (called as conduction current)

and the time varying electric flux. Mathematically

…(i)

where B is the magnetic field, dl is small element of length of an

Amperian loop, μ_{0} is the magnetic permeability of free space and its value is 4π × 10^{-7} T m A^{-1}, I_{enclosed} is the current due to charge carriers (conduction current) and I_{d} is the displacement current which

is related to changing electric field.

The displacement current is related to electric field as

…(ii)

where *ϕ*_{E} is the time varying electric flux through the surface

and *ϵ*_{0} is the electric permittivity of free space(vacuum) and is equal

to 8.85 × 10^{-12} C^{2} N^{-1} m^{-2}.

The electric flux is the amount of electric field lines passing

through a surface normally. Mathematically

…. (iii)

where E(t) is the time varying electric field, dS are a small area

element on the surface and θ is the angle between the electric field

vector and area vector (if the field lines are not falling normally).

From (ii) and (iii)

If the conduction current is zero, so the magnetic field will entirely be

produced by the changing electric field and would be produced by it.

Hence B. is correct

Hence D. is correct

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