This page explains how to find the Hawa Koth shrine and solve the "The Current Solution" puzzle.
How to Reach the Shrine
This shrine is southwest of Gerudo Town, so go to Daqo Chisay Shrine and go southwest from there. You will encounter a sandstorm on the way. You may find it easier to get there on a sand seal, which you can rent in Gerudo Town, or you can sneak up on a seal in the wild to hitch a ride.
How to Solve the Shrine
Use Magnesis to put the metal boxes onto the short pillars between the green electricity source and the orange light. This will open the gate. The gate will stay open even if the electricity stops flowing.
When you go through the gate, look to the right and use Magnesis to lift the treasure chest out of the water. It contains an Ancient Core.
Then use Magnesis to untangle the chain from the pillars, and move the metal ball to the orange light near the wall. This will make the platform rise and fall.
Go up the platform and use Magnesis on the green ball. You can dump the three Guardian Scouts into the water by moving the green ball onto the orange lights near the Guardian Scouts.
Then put the green ball onto the platform to the right of where the Guardian Scouts were. A panel in the wall will move. Walk across it and open the chest that you find there to get a Gold Rupee.
Then go back to where the Guardians were and move the green ball next to the orange light near the bars. A gear will start turning, but the bars won't open.
Look to the right of the bars to see an archway. Go through, and step on the switch to slide the blocks away. Then use Magnesis to slide the metal blocks to the right so that they are in the way of the rightmost column of blocks. Then get off of the switch. The leftmost and rightmost wires should be in line with the electric current, but not the middle. Use Magnesis to push that wire in line with the other two. Hold it there until the nearby bars open.
Use Magnesis to lift the gear inside of the bars. Open the chest there to get a sapphire. Then move the gear into place above the bars that are blocking you from reaching Hawa Koth. When the bars open, go in and talk to Hawa Koth to get the Spirit Orb.