The following Matrix Match type question which appeared in the IIT-JEE 2007 question paper aims at checking your understanding of basic principles of electricity and magnetism. Here is the question:
Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4×4 matrix given in the OR
Column I------------------------------ Column II
(A) A charged capacitor is---------------(p) A constant current flows
connected to the ends of---------------- through the wire
the wire
(B) The wire is moved -----------------(q) Thermal energy is generated
perpendicular to its length with -------- in the wire
a constant velocity in a uniform
magnetic field perpendicular to
the plane of motion
(C) The wire is placed in a constant ---(r) A constant potential
electric field that has a direction ------difference develops between
along the length of the wire-----------the ends of the wire
(D) A battery of constant emf is ------(s) Charges of constant
connected to the ends of the----------magnitude appear at the ends
wire ---------------------------------of the wire
(A) When a charged capacitor is connected to the ends of a wire, a discharge current flows through the wire and the wire is heated. This is given in statement (q) under column II so that (A) is to be matched with (q).
(B) When the wire is moved perpendicular to the magnetic field, free electrons in the wire experience a magnetic (Lorentz) force and shift towards one end. Consequently, a potential difference develops between the ends of the wire. Since the wire is moving with constant velocity in a constant magnetic field, the charges developed at the ends as well as the potential difference between the ends are constant. Therefore, (B) is to be matched with (r) and (s).
(C) When the wire is placed in the electric field, free electrons shift towards the end of the wire which is at higher potential. This shifting of free electrons results in the accumulation of charges at the ends of the wire. But there is no potential difference between the ends of the wire since the shifting of free electrons just nullifies the potential difference caused by the external electric field. Therefore, (C) is to be matched with (s) only.
(D) When a battery of constant emf is connected to the ends of the wire, the effects given at (p) (q) and (r) under Column II occur. Therefore, (D) is to be matched with (p), (q) and (r).
These are to be marked in the 4×4 matrix as shown:
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