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Pq And Rs Are Long Parallel Conductors Separated By Certain Distance. M Is The Midpoint Between Them. The Net Magnetic Field At M Is B. Now The Current 2 A Is Switched Off. The Field At M Now Becomes
PQ and RS are long parallel conductors separated by a certain distance. M is the midpoint between them. The net magnetic field at M is B. Now the current 2 A is switched off. The field at M now becomes.
The problem statement is asking us to find the magnetic field at point M when the current in wire PQ is switched off. We can solve this problem by using the Biot-Savart law.
The Biot-Savart law states that the magnetic field due to a current-carrying conductor at a point is directly proportional to the current flowing through the conductor and inversely proportional to the distance between the point and the conductor.
Let’s consider the magnetic field due to wire PQ first. Using the Biot-Savart law, we can write:
B_PQ = (μ_0 / 4π) * (2 I / d)
where μ_0 is the permeability of free space, I is the current flowing through wire PQ, and d is the distance between wire PQ and point M.
Similarly, we can find the magnetic field due to wire RS:
B_RS = (μ_0 / 4π) * (I / d)
where I is the current flowing through wire RS.
Since wire PQ and wire RS are parallel and carry currents in opposite directions, their magnetic fields at point M will be in opposite directions as well. Therefore, we can write:
B_net = B_PQ – B_RS
Substituting the values of B_PQ and B_RS, we get:
B_net = (μ_0 / 4π) * (2 I / d) – (μ_0 / 4π) * (I / d)
B_net = (μ_0 / 4π) * (I / d)
Now that we have found the magnetic field at point M due to wire PQ and wire RS when both are carrying currents, we can find the magnetic field at point M when the current in wire PQ is switched off.
When the current in wire PQ is switched off, only wire RS will be carrying current. Therefore, we can write:
B_new = (μ_0 / 4π) * (I / d)
which is equal to B_net.
Therefore, when the current in wire PQ is switched off, the magnetic field at point M will remain unchanged and will be equal to B_net.
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