Question

A circular loop of radius a, carrying a current i, is placed in a two-dimensional magnetic field. The centre of the loop coincides with the centre of the field (figure). The strength of the magnetic field at the periphery of the loop is B. Find the magnetic force on the wire.
Figure

Answer 1

Answer:

Bi2pir

Explanation:

as solve in figure as given above

Answer 2

The magnetic force on the wire is i2πaB.

Explanation:

It is given:

The radius of a circular loop = a

So, the loop’s length, l = 2πa

Electric current passing via the loop = i

As mentioned in the question,

• In a magnetic field of two-dimensions, the loop is placed. The loop center coincides with the field center. The magnetic fields at the loop’s periphery are B
• So, the magnetic field focuses on outwardly outwards.
• Now, the angle between the magnetic field and the loop’s length, θ = 90Ëš

Magnetic force is shown as

F→ = il→$\times$B→F →

= i2πa$\times$B→F→  

= i2πaB

• Using Fleming’s left-hand rule, the force’s direction can be found.
• Therefore, the magnetic force’s direction is perpendicular to the figure’s plane and pointing inwards.