Step 1 :Given values: B = 0.25 T, L = 0.75 m, v = 8.0 m/s, R = 5.0 Ω
Step 2 :Calculate the induced EMF using the formula EMF = B * L * v
Step 3 :EMF = 0.25 T * 0.75 m * 8.0 m/s = \(1.5 V\)
Step 4 :Calculate the current using Ohm's law: I = EMF / R
Step 5 :I = \(\frac{1.5 V}{5.0 Ω}\) = \(0.3 A\)
Step 6 :Use the right-hand rule to find the direction of the current
Step 7 :Since the magnetic field is going into the plane of the paper, and the rod is moving to the right, the current will be going to the left
Step 8 :\(\boxed{\text{Final Answer: The magnitude of the current is 0.3 A, and the direction of the current through point X is to the left.}}\)