What solid state relay would I need for flashing on and off over prolonged period of time?

Im running a 12v power pack with 10amps DC! The circuit is nothing more than 100 Meters of single core copper wire at 1.5mm. Ohms resistance is 1.4 - I require that the power going through my wire turn on and off to help magnets pulse and release for a science project. The relay will be in use for 1 hour to 1 hour and 30 minutes at a time. I was previously using regular car flasher but they tend to break after 3 weeks of use - ive been informed on this website that a solid state relay would be the better option. Thank you.

The reason the mechanical relays tend to break when switching continuously like this is that the contacts and mechanical parts are only rated for a certain number of switching operations at a given current. Each time the switch moves, it generates a tiny electrical arc that corrodes the contacts. That arc becomes more significant at higher currents, which shortens the number of switching operations that the mechanical relay can survive.

A solid state relay (SSR) doesn't have any mechanical parts, so you can switch them on and off as many times as you like with no real impact on operational lifetime. As long as you're operating it below the maximum specifications, it should last pretty much forever.

In terms of what specifications you need, a general rule of thumb is to double the normal operating voltage and current. So, for a 12V 10A load, go for an SSR that is rated for at least 24V DC and 20A, as a bare minimum. That way you have some headroom. The other thing you'll want to check is what control voltage is needed to turn the SSR on or off. The datasheet will have a minimum and maximum voltage for that input, e.g. 5V to 15V.

You will also need a flyback diode to protect against flyback currents. An electromagnet is an inductive load, and when you turn off the SSR it'll create a voltage spike as the inductor discharges. By putting a diode in reverse over the load it'll dissipate (or "snub") that voltage spike and protect the SSR. Schottky diodes are generally preferred for this.

In your case you don't really need an SSR module - you can build the whole thing very cheaply with a single N-channel MOSFET and a 10kΩ resistor.

simulate this circuit – Schematic created using CircuitLab

Picking the right MOSFET here is a bit involved, so I'll save the long explanation and just recommend an IRFB7430 here since it's easily available and will operate properly when driven by any control voltage from 5V to 20V. It might get a bit warm (~50°C) if you use 5V signals to control it, but that's well within its operating spec. At 6V or higher on the gate it'll barely get above room temperature.

You can pick pretty much any Schottky diode here. Something like an SR360, SB560, or SB5100 will work fine.

search for "arduino mosfet driver circuit" (if you type "arduino" in front of any electronics question you will get the easier to understand results) and you will find lots of diagrams like this: https://www.gammon.com.au/images/MOSFET_low_side_driver.png

N channel MOSFET + some resistors + protection diode. The "load" is your electromagnet