Two parallel wires carry 1-A currents in unknown directions. The distance between the wires is 10-cm. What is the magnitude of the magnetic field B in Teslas at a point P located 6-cm away from the axis of one of the wires and 8-cm away from the axis of the other wire?

Unot=4pi×10^-7

Hint: your teacher made a 3-4-5 triangle for you, which means the two B fields are at 90 degrees to each other, so when they add or subtract, magnitude does not change, just direction.

Find B from each, and then add them as 90 degree vectors..

c= sqrt(a^2+b^2)

Can't get it, Didn't studied this topic, Would you please work the solution.

But radius is not given

To find the magnitude of the magnetic field B at point P, we can use the Biot-Savart Law, which states that the magnetic field created by a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.

The formula for the magnitude of the magnetic field created by a current-carrying wire is given by:

B = (μ0 * I) / (2π * r)

Where:
B is the magnetic field in Teslas (T)
μ0 is the permeability of free space, equal to 4π × 10^-7 T·m/A
I is the current in Amperes (A)
r is the distance from the wire in meters (m)

In this case, we have two parallel wires carrying a 1-A current in unknown directions, and the distance between the wires is 10-cm. Point P is located 6-cm away from the axis of one wire and 8-cm away from the axis of the other wire.

To find the magnetic field at point P, we need to find the magnetic fields created by each wire and then add them up.

First, let's find the magnetic field created by the wire located 6-cm away from point P. We can use the formula:

B1 = (μ0 * I) / (2π * r1)

Where:
B1 is the magnetic field created by the first wire
r1 is the distance from point P to the first wire (6-cm = 0.06-m)

Substituting the values we know:

B1 = (4π × 10^-7 T·m/A * 1 A) / (2π * 0.06 m)

Simplifying the equation:

B1 = 10^-6T

Now, let's find the magnetic field created by the wire located 8-cm away from point P. We can use the same formula:

B2 = (μ0 * I) / (2π * r2)

Where:
B2 is the magnetic field created by the second wire
r2 is the distance from point P to the second wire (8-cm = 0.08-m)

Substituting the values we know:

B2 = (4π × 10^-7 T·m/A * 1 A) / (2π * 0.08 m)

Simplifying the equation:

B2 = 10^-6T

Now, we can find the total magnetic field at point P by adding the magnetic fields created by each wire:

B = B1 + B2
B = 10^-6T + 10^-6T
B = 2 * 10^-6T
B = 2 μT (microteslas)

Therefore, the magnitude of the magnetic field at point P is 2 microteslas (2 μT).