Q. 12

# 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.

Given –

circular loop of radius = a

So, the length of the loop is its circumference ,

Electric current through the loop = i

Given that the loop is placed in a two-dimensional magnetic field.

Also the centre of the loop coincides with the centre of the field.

The strength of the magnetic field at the periphery of the loop is B

Hence, the direction of the magnetic is radially outwards.

Here, the angle between the length of the loop and the magnetic field, θ = 900

where,

B= magnetic field

I = current

l = length of the wire

and θ = the angle between B and l

The direction of force can be found using Fleming’s left-hand rule -

whenever a current carrying conductor is placed inside a magnetic field, a force acts on the conductor, in a direction perpendicular to both the directions of the current and the magnetic field

Thus, the direction of magnetic force lies perpendicular to the plane pointing inwards.

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