Question

Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects
are described in Column II. Match the statements in Column I with the statements in Column II and indicate your
answer by darkening appropriate bubbles in the 4X4 matrix given in the ORS.

Answer 1

We can find the direction of magnetic field at P due to a wire by the corkscrew rule, and the direction of force on a wire due to other is calculated by the direction of cross product of direction of current and direction of magnetic field.

$F=Q\overrightarrow{l}\times \overrightarrow{B}$

Option A-(q) (r)

By thumb rule, the magnetic field lines at P due to both wires are in opposite direction. and since it's midpoint, they're equal and opposite by symmetry, hence resultant field is zero.

The direction of force on each wire is towards each other, as it can be seen from the above equation, hence they attract each other.

Option B-(p)

By thumb rule(apply on infinitesimal parts for the sense of direction of magnetic field ), the magnetic field lines at P due to both wires are in same direction.

The wires neither attract nor repel

Option C- (q) (r)
By thumb rule, the magnetic field lines at P due to both wires are in opposite direction. and since it's midpoint, they're equal and opposite by symmetry, hence resultant field is zero.

The direction of force on each wire is towards each other, as it can be seen from the above equation, hence they attract each other.

Option D- (q)

By thumb rule, the magnetic field lines at P due to both wires are in opposite direction. and since the radius is different, the resultant field is non-zero and n opposite direction..