A power line 10 meter high carries a current 200 amperes .Find the magnetic field of the wire at ground?

4*10^-6

Oh, I see you're trying to shock me with this electrifying question! Well, let me entertain you with a magnetic response.

The magnetic field generated by a wire is given by Ampere's law. For a long, straight wire carrying a current, the magnetic field at a distance R from the wire is approximately μ₀ times the current divided by 2π times the distance to the wire. Where μ₀ is the permeability of free space, approximately equal to 4π × 10⁻⁷ Tesla meter per ampere (T·m/A).

So, in this shocking scenario, the current is 200 amperes and the wire is 10 meters high above the ground. Let's say we're at the ground, right below the wire.

If we assume the wire is a straight line, we can use the formula to calculate the magnetic field. Plugging in the values, we get:

B = (μ₀ × I) / (2π × R)

Where I is the current and R is the distance from the wire (in this case, it's the height of the wire, 10 meters).

Now, we can plug the numbers in:

B = (4π × 10⁻⁷ T·m/A × 200 A) / (2π × 10 m)

We can simplify it further:

B = (8 × 10⁻⁶ T·m) / (20π m)

Finally, we can calculate the value:

B ≈ 0.000127 T

So, my electrifying friend, the magnetic field of the wire at ground level is approximately 0.000127 Tesla. Just enough to give you a "shocking" experience!

To find the magnetic field of a wire at a point on the ground, we can use Ampere's law.

Ampere's law states that the magnetic field (B) around a closed loop is proportional to the current (I) passing through the loop.

In this case, we will consider a circular loop around the wire at the ground. The magnetic field will be perpendicular to the loop.

Assuming the wire is infinitely long, we can consider a circular loop with a radius (r) centered at the wire. Let's calculate the magnetic field at the center of this loop.

The formula for the magnetic field at the center of the loop due to a long straight wire is given by:

B = μ0 * I / (2π * r)

where B is the magnetic field, μ0 is the permeability of free space (4π x 10^-7 Tm/A), I is the current, and r is the radius.

In this case, the current I is given as 200 amperes, and we have to calculate the radius r.

Considering a right-angled triangle, where the height of the wire is 10 meters, and the radius is the hypotenuse, we can use Pythagoras' theorem to calculate the radius.

Using Pythagoras' theorem, we have:

r = √(h^2 - d^2)

where h is the height of the wire and d is the distance of the loop from the wire.

In this case, h = 10 meters and d = 0 meters (since the loop is at the ground).

Substituting the values, we get:

r = √(10^2 - 0^2) = √100 = 10 meters

Now, we can substitute the values of I and r into the equation for the magnetic field:

B = (4π x 10^-7 Tm/A) * 200 A / (2π * 10 m)

Simplifying further:

B = (2 x 10^-7 Tm/A) * 200 A / 10 m
B = (2 x 10^-7) * 200 / 10 T
B = (2 x 2 x 10^-7) T
B = 4 x 10^-7 T

Thus, the magnetic field of the wire at the ground is 4 x 10^-7 Tesla.

To find the magnetic field produced by the power line at ground, we can use Ampere's Law. Ampere's Law states that the integral of the magnetic field around a closed loop is equal to the product of the current passing through the loop and the permeability of free space.

Mathematically, it can be expressed as:

∮ B · dl = μ₀ * I,

where B is the magnetic field, dl is a small element of the closed loop, μ₀ is the permeability of free space (4π × 10^-7 T·m/A), and I is the current passing through the loop.

In this scenario, we can consider a circular loop on the ground, centered underneath the power line. The height of the power line is given as 10 meters, which means the circular loop on the ground will also have a radius of 10 meters.

The current passing through the loop is given as 200 amperes.

Applying Ampere's Law, we can calculate the magnetic field at ground:

∮ B · dl = μ₀ * I,

B * 2π * R = μ₀ * I,

B = (μ₀ * I) / (2π * R),

where R is the radius of the circular loop.

Plugging in the values, we get:

B = (4π × 10^-7 T·m/A * 200 A) / (2π * 10 m),

B = (8 × 10^-5) / (20),

B = 4 × 10^-6 Tesla.

Therefore, the magnetic field produced by the power line at ground is 4 × 10^-6 Tesla.

Wonder where the return current is flowing? Ground?

Ok, assuming power can be transmitted by only one wire, then Ampere's law applies

INT B.ds=mu*I
B*2Pi*10=mu*200
solve for B