rectangular loop of wire of mass and resistance slides on a friction-free horizontal table. There is a region of uniform magnetic field perpendicular to the table as shown. what type of graph will descfibe the speed of the loop as a function of time?
To determine the type of graph that describes the speed of the loop as a function of time, we need to consider the forces acting on the loop.
In this scenario, the loop of wire is moving in a uniform magnetic field, which will induce an electromotive force (emf) in the loop according to Faraday's law of electromagnetic induction. This emf will cause an electric current to flow in the loop.
Due to the resistance of the wire, the current flowing through it will cause a resistive force opposing the motion of the loop. According to Ohm's law, the current is directly proportional to the emf and inversely proportional to the resistance.
Now, since the loop is initially at rest and there is no friction or external force acting on it, the only force present is the resistive force due to the induced current.
The resistive force acts in a direction opposite to the motion of the loop, so initially, when the current starts flowing, the resistive force will be at its maximum and the loop will experience a deceleration. As time progresses and the magnitude of the current decreases due to the loop's resistance, the resistive force will also decrease. This will result in a decrease in the deceleration of the loop until finally, when the current becomes constant (at a steady state), the resistive force will also become constant, and the loop will reach a constant speed.
Therefore, the graph of the speed of the loop as a function of time will first show a decrease in speed (negative acceleration) until it reaches a minimum value, and then it will remain constant.
In summary, the graph will show a decreasing slope initially, representing the deceleration, followed by a horizontal line representing the constant speed of the loop once it reaches a steady state.