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Two circular coils can be arranged in any of the three situations shown in figure. Their mutual inductance will be,
- a)maximum in situation (i).
- b)maximum in situation (ii).
- c)maximum in situation (iii).
- d)the same in all situations.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two circular coils can be arranged in any of the three situations show...
Let the radius of bigger coil be R and radius of smaller coil be r. Let I be the current passing through the bigger coil in anti-clockwise direction.
Magnetic field produced due to circular coil at its centre is vertically upwards.
Let M be the mutual induction of the coils. Then, we can write,
Here, ϕ = magnetic flux.
Since, ϕ = BAcos(θ), we can write,
In case of (i): Magnetic field due to bigger coil and surface vector of smaller coil lies in same direction, i.e., θ = 0°
In case of (ii): Magnetic field due to bigger coil and surface vector of smaller coil perpendicular to each other, i.e., θ = 90°
In case of (iii): No field line passes through the smaller coil since the smaller coil is placed beside bigger coil and B is vertically upwards. Hence, the field at centre of smaller coil will be zero.
By comparing equation (1), (2) and (3), we can write,
Hence, mutual inductance is maximum in situation (i).
Magnetic field produced due to circular coil at its centre is vertically upwards.
Let M be the mutual induction of the coils. Then, we can write,
Here, ϕ = magnetic flux.
Since, ϕ = BAcos(θ), we can write,
In case of (i): Magnetic field due to bigger coil and surface vector of smaller coil lies in same direction, i.e., θ = 0°
In case of (ii): Magnetic field due to bigger coil and surface vector of smaller coil perpendicular to each other, i.e., θ = 90°
In case of (iii): No field line passes through the smaller coil since the smaller coil is placed beside bigger coil and B is vertically upwards. Hence, the field at centre of smaller coil will be zero.
By comparing equation (1), (2) and (3), we can write,
Hence, mutual inductance is maximum in situation (i).
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Two circular coils can be arranged in any of the three situations shown in figure. Their mutual inductance will be,a)maximum in situation (i).b)maximum in situation (ii).c)maximum in situation (iii).d)the same in all situations.Correct answer is option 'A'. Can you explain this answer?
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