Two concentric and coplanar circular loops P and Q have theirradii in the ratio 2:3. Loop Q carries a current 9 A in theanticlockwise direction. For the magnetic field to be zero at thecommon centre, loop P must carry(i) 3A in clockwise direction(ii) 9A in clockwise direction(iii) 6 A in anti-clockwise direction(iv) 6 A in the clockwise direction.

The magnetic field at the center of a circular loop due to the current flowing in it is given by the formula B = μ0I/2R, where B is the magnetic field, μ0 is the permeability of free space, I is the current, and R is the radius of the loop.

Given that the radii of the loops P and Q are in the ratio 2:3, let's denote the radius of loop P as 2r and the radius of loop Q as 3r.

The magnetic field at the center due to the current in loop Q is BQ = μ09/23r = 3μ0/r.

For the magnetic field to be zero at the center, the magnetic field due to the current in loop P must be equal and opposite to BQ. Let's denote the current in loop P as IP. So we have:

BP = -BQ μ0IP/22r = -3μ0/r IP = -3*4 = -12 A

The negative sign indicates that the current must flow in the opposite direction to the current in loop Q. Since the current in loop Q is flowing in the anticlockwise direction, the current in loop P must flow in the clockwise direction.

So, for the magnetic field to be zero at the common center, loop P must carry 12 A in the clockwise direction. However, this option is not given in the choices. There might be a mistake in the problem or the given choices.