By 1898 a rear wheel drive electric bicycle, which used a driving belt along the outside edge of the wheel was patented by Mathew J. Steffens. Also, the 1899 Template:US Patent by John Schnepf depicted a rear wheel friction “roller-wheel” style drive electric bicycle.[5] Schnepf's invention was later re-examined and expanded in 1969 by G.A. Wood Jr. with his Template:US Patent. Wood’s device used 4 fractional horsepower motors; each rated less than ½ horsepower and connected through a series of gears.[6]
Great question… a real world situation from someone doing their best to follow the law but also be realistic about time/distance. What follows is my opinion on the matter based on lots of electric bike riding experience, this is not legal advice. You can probably ride with electric assist across the dirt way with no issues and avoid any negative response that might arise as long as you’re polite to other cyclists and pedestrians and pedal along without going too fast. If someone called you out about it you could easily hop off, walk your bike and explain that you use the assist to help make your commute possible or possibly, like me, you have a knee injury and it’s difficult to pedal through softer terrain like gravel. Another different approach might be to shut the bike off completely before entering the gravel section, you could even take the battery off and put it in a backpack or as mentioned earlier… just walk the bike. Imagine if you had a motorized dirt bike and were just pushing it along a sidewalk… this kind of vehicle definitely is not allowed on sidewalks or most gravel paths like the one you’re describing but if you were escorting it carefully, you’d be honoring the spirit of the law and if an officer or pedestrian jumped out and started questioning you about your “motorized vehicle” it is my feeling that a genuine explanation and apology or request for guidance would go very well. I personally have never had issues riding electric bikes in part because I am thoughtful about how I use them. I do occasionally switch them off and sometimes I get off and walk. I have asked police in many cities across the US what they thought about ebikes and in every case I have received positive interest and support with guidance to ride safe with a helmet and follow traffic laws in the street. I hope this helps and I wish you well, it’s nice that you care enough to ask and I hope you’re treated well by others out on the road. The flip side of this response is that I have been harassed, yelled at and even swerved at by automobiles when riding bicycles and electric bikes. This usually happens in the evening after work lets out when traffic is heavy and I’m riding on the shoulder or in the street (where marked to do so) and I believe it has to do with territory, testosterone and socio-economic standing more so than laws or anything like that.
Depending on local laws, many e-bikes (e.g., pedelecs) are legally classified as bicycles rather than mopeds or motorcycles. This exempts them from the more stringent laws regarding the certification and operation of more powerful two-wheelers which are often classed as electric motorcycles. E-bikes can also be defined separately and treated under distinct Electric bicycle laws.
On February 4, 2014, SB997 was introduced by Senator Matt Smith, which seeks to amend PA Vehicle Code to include "Pedalcycle with Electric Assist". In a memo addressed to all senate members, Smith said the definition shall include "bicycles equipped with an electric motor not exceeding 750 watts, weighing not more than 100 pounds, are capable of a maximum speed of not more than 20 mph, and have operable pedals."[128][129]
In a friction drive motor, a small, solid wheel rotates against the side of the tire in order to drive it. The first motorcycles used the same concept, with a motor mounted above the front wheel. The problem is that the drive rubs at the side of the tire. It's inefficient, and it quickly wears the sidewall away. Tires need to be replaced every couple hundred miles. For this reason, you'll seldom see electric bikes with this type of drive anymore.

"Bicycles" and "Electric Bicycles" are legally defined in the Texas Transportation Code Chapter 551., titled "Operation of Bicycles, Mopeds, and Play Vehicles" in Subchapter A, B, C, and D.[58] The following definition of electric bicycle was passed by the Texas legislature in 2001. "Electric bicycle" means a bicycle that is designed to be propelled by an electric motor, exclusively or in combination with the application of human power, cannot attain a speed of more than 20 miles per hour without the application of human power; and does not exceed a weight of 100 pounds. The department or a local authority may not prohibit the use of an electric bicycle[0] on a highway that is used primarily by motor vehicles. The department or a local authority may prohibit the use of an electric bicycle[0] on a highway used primarily by pedestrians.
And let’s not forget the economic advantages of owning an e-bike. The annual cost of running a new family car is, on average, about $9,000 per year. Running an electric bike costs around $400 per year. And while filling a gas tank costs around $30, recharging an electric bike battery costs only about 50 cents. A tank of gas may get you further, but not 60 times further!
The legal definition/description of an electric bicycle is most closely described in the code as a "motorized scooter" in that it is powered by an electric motor and/or human power [45]. It may be also be described as a "Motorized bicycle". However, that description does not include electric powered motor specifically. And it appears that the legal definition "Motorized Bicycle" and "Motorized Scooter" are in conflict. Motorized bicycle is a pedal bicycle which has a helper motor, or a non-pedal bicycle which has a motor, with a cylinder capacity not exceeding fifty cubic centimeters, an automatic transmission, and which is capable of a maximum speed of no more than thirty miles per hour. A motorized bicycle shall not be operated upon any way, as defined in section one within the commonwealth by any person under sixteen years of age, nor at a speed in excess of twenty-five miles per hour. A motorized bicycle shall not be operated on any way by any person not possessing a valid driver’s license or learner’s permit. Every person operating a motorized bicycle upon a way shall have the right to use all public ways in the commonwealth except limited access or express state highways where signs specifically prohibiting bicycles have been posted, and shall be subject to the traffic laws and regulations of the commonwealth and the regulations contained in this section, except that the motorized bicycle operator may keep to the right when passing a motor vehicle which is moving in the travel lane of the way, and the motorized bicycle operator shall signal by either hand his intention to stop or turn. Motorized bicycles may be operated on bicycle lanes adjacent to the various ways, but shall be excluded from off-street recreational bicycle paths. Every person operating a motorized bicycle or riding as a passenger on a motorized bicycle shall wear protective headgear conforming with such minimum standards of construction and performance as the registrar may prescribe, and no person operating a motorized bicycle shall permit any other person to ride a passenger on such motorized bicycle unless such passenger is wearing such protective headgear.
Oregon Law (ORS 801.258]) defines an electric assisted bicycle as an electric motor-driven vehicle equipped with operable pedals, a seat or saddle for the rider, no more than three wheels in contact during travel. In addition, the vehicle must be equipped with an electric motor that is capable of applying a power output of no greater than 1,000 watts, and that is incapable of propelling the vehicle at a speed greater than 20 miles per hour on level ground.[124]
The headlight/horn is completely frail, and prevents folding the bike. However, the wires broke off within two days (60 miles) of riding, so it wasn't an issue after I removed the light completely. Other than that, it's a great electric bike. I put about 24-40 miles per day on it, and it does the job well. I have steep hills during my ride and it really helps with the effort required to go uphill. The gears only go up to 7, which means that when on flat ground, and pedaling for all that I'm worth, I can only get up to 19 mph before the pedals just spin madly. I pass other cyclists when going uphill at nearly twice their speed, but not so much on flat ground or downhill. The rear has no suspension at all, so I bought a $50

On the other hand, the battery doesn’t lock into the bike, which means you can’t just leave it on your bike when you park at the bike rack. Anyone could walk by and simply remove your battery. That seems like an oversight to me, though perhaps the designers assumed that such a small battery would just be easy to take with you. And it is. My wife could probably lose this battery in her purse.