CBSE Class 12 Physics 2019 Delhi Set 3 Paper

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Question : 7
Total: 8
Two infinitely long straight wires A1 and A2 carrying currents I and 2I flowing in the same direction are kept ' d ' distance apart. Where should a third straight wire A3 carrying current 1.5I be placed between A1 and A2 so that it experiences no net force due to A1 and A2 ? Does the net force acting on A3 depend on the current flowing through it?
Solution:  
Finding the position of third wire
Reason

⇒‌‌F1‌=‌
µ0
4Ï€
‌
I×1.5I
x

F2‌=‌
µ0
4Ï€
‌
2I×1.5I
(d−x)

For no force on the conductor A3
‌
µ0
4Ï€
‌
I×1.5I
x
‌
=‌
µ0
4Ï€
‌
2I×1.5I
(d−x)

‌
1
x
‌
=‌
2
(d−x)

3x‌=d
x‌=‌
d
3
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