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Question
A loop of flexible conducting wire lies in a magnetic field of 4.0 T with its plane perpendicular to the field. The length of the wire is 1 m. When a current of 2.2 A is passed through the loop, it opens into a circle, then the tension developed in the wire is ____________.
Options
0.5 .N
0.25 N
1.4 N
0.4 N
Solution
A loop of flexible conducting wire lies in a magnetic field of 4.0 T with its plane perpendicular to the field. The length of the wire is 1 m. When a current of 2.2 A is passed through the loop, it opens into a circle, then the tension developed in the wire is 1.4 N.
Explanation:
As the coil is perpendicular to magnetic field
`vec "B" = 2 "T",`
`theta = 90°`
The loop formed is circular,
`therefore l = 2 pi"r"`
As the force acting on the loop will be along radius,
`"r" = l/(2pi)`
∴ Tension developed is
`"T" = "F" = "B" "I" "r sin" theta = "B" "I" "r"`
`= (4 xx 2.2 xx l)/(2pi)`
` = 4.4/pi`
` = 1.4 "N"`
