Derive an expression for the current in a system like that in figure below, under the following conditions. The resistance between the rails is R , the rails and the moving rod are identical in cross section A and have the same resistivity ρ. The distance between the rails is l, and the rod moves at constant speed v perpendicular to the uniform field B. At time zero, the moving rod is next to the resistance R.
The expression is
According to Lenz, the direction of induced emf and hence the direction of the induced current is such that it will oppose the motion of the conductor in the external field.
The current (I) can be calculated using Ohm's law, as-
Where is emf and R is Resistance.
The emf will be given as
The resistance (R) of the metal structure, which means,
Combining the two expressions, we get,
The above equation can further be expressed as-
This is the required expression.
(a) An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner’s 2.00 T field with his fingers pointing in the direction of the field. Find the average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field. (b) Discuss whether this current would significantly change the temperature of the ring.
When a magnet is thrust into a coil as in Figure 23.4(a), what is the direction of the force exerted by the coil on the magnet? Draw a diagram showing the direction of the current induced in the coil and the magnetic field it produces, to justify your response. How does the magnitude of the force depend on the resistance of the galvanometer?
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