The conducting rod ab shown below makes frictionless contact with metal rails ca and db. The apparatus is in a uniform magnetic field of 0.855 T, perpendicular to the plane of the figure. The length L of the rod is 25 cm. (a) Find the magnitude of the emf induced in the rod when it is moving towards the right with a speed of 6.50 m/s. (b) In what direction does the current flow in the rod (clockwise or counter-clockwise)? Write several sentences that clearly explain your reasoning. (c) If the resistance of the circuit abdc is a constant 3.5 Ω, find the magnitude and direction of the force required to keep the rod moving to the right with a constant speed of 6.5 m/s.
The conducting rod ab shown below makes frictionless contact with metal rails ca and db. The apparatus is in a uniform magnetic field of 0.855 T, perpendicular to the plane of the figure. The length L of the rod is 25 cm. (a) Find the magnitude of the emf induced in the rod when it is moving towards the right with a speed of 6.50 m/s. (b) In what direction does the current flow in the rod (clockwise or counter-clockwise)? Write several sentences that clearly explain your reasoning. (c) If the resistance of the circuit abdc is a constant 3.5 Ù, find the magnitude and direction of the force required to keep the rod moving to the right with a constant speed of 6.5 m/s.
To find the magnitude of the EMF induced in the rod, we can use the formula EMF = B * L * v, where B is the magnetic field strength, L is the length of the rod, and v is the velocity of the rod.
Given that the magnetic field strength is 0.855 T and the length of the rod is 25 cm (or 0.25 m), and the velocity is 6.50 m/s, we can substitute these values into the formula to find the magnitude of the induced EMF.
EMF = 0.855 T * 0.25 m * 6.50 m/s
EMF = 1.10625 V
Therefore, the magnitude of the induced EMF is 1.10625 volts.
To determine the direction of the current flow in the rod, we can use the right-hand rule. If we point our right thumb in the direction of the velocity of the rod (to the right in this case), and our fingers curl in the direction of the magnetic field (perpendicular to the plane of the figure and into the page as indicated), then the direction in which the palm of our hand faces represents the direction of the current flow.
In this case, the palm of our hand would face downward, which indicates that the current flows in a clockwise direction in the rod.
To calculate the magnitude and direction of the force required to keep the rod moving to the right with a constant speed of 6.5 m/s, we can use the equation F = I * R, where F is the force, I is the current, and R is the resistance.
From part (a), we found that the magnitude of the induced EMF is 1.10625 V. Since the resistance of the circuit abdc is given as 3.5 Ω, we can determine the current by dividing the magnitude of the induced EMF by the resistance.
I = EMF / R
I = 1.10625 V / 3.5 Ω
I = 0.316 A
Therefore, the magnitude of the current is 0.316 amperes.
Since the rod is moving to the right and the current flows clockwise (as determined in part (b)), we can apply the right-hand rule again to determine the direction of the force. Pointing our right thumb in the direction of the current (clockwise) and our other fingers in the direction of the magnetic field (perpendicular to the plane of the figure and into the page as indicated), the direction in which our palm faces represents the direction of the force.
In this case, the palm of our hand would face upward, which indicates that the force required to keep the rod moving to the right with a constant speed of 6.5 m/s is upward.