A non conducting square plate 75 cm on a side carries a uniform surface charge density. The electric field strength 1 cm from the plate, not near an edge, is 45 kN/C. Whats the approximate field strength 15 m from the plate?

 E = 5.03 10⁻³ N / C

Explanation:

For this exercise we can use Gauss's law

         Ф = E. dA = /ε₀

Where as a Gaussian surface we select a cylinder

         Ф= E A = q_{int} /ε₀

Let's use the concept of surface charge density

         σ = q / A

         q = σ A

         E A = σ A /ε₀  

         E = sig /ε₀

Since the plate is non-conductive, the fux does not flow through the plate

With this equation the electric field does not depend on the distance, so the field at 1 cm

              E = 45 10³ N/C

             σ = E ε₀  

             σ = 45 10³  8.85 10⁻¹²

             σ = 3.98 10⁻¹⁰ C / m²

As the point where the field is requested is very far from the plate we can not ignore the finite size of it

At r = 15 m the plate has a very small size, so let's calculate the field as created by a point load at this distance

           E = k q / r²

The plate area is

            A = L L

            A = 0.75²

            A = 0.5625 m²

            q = σ A

            q = 3.98 10⁻¹⁰ 0.5625

            q = 1.26 10⁻¹⁰ C

Let's calculate

            E = 8.99 10⁹  1.26 10⁻¹⁰ / 15²

            E = 5.03 10⁻³ N / C

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it

explanation:

wheres the pic