Two charged particles have equal mass and carry charges of 2 nC and 3 nC respectively. They enter a magnetic field of strength 2 mT at the same velocity.

Assuming that both particles exit the field parallel to each other and perpendicular to the field, determine the separation of the particles on exiting the field if the circular path followed by the 3 nC particle is 12 cm.

To determine the separation of the particles on exiting the magnetic field, we need to use the concepts of the magnetic force and the circular motion of charged particles in a magnetic field.

The magnetic force on a charged particle moving in a magnetic field is given by the equation:

F = q * v * B * sin(θ)

Where:
F is the magnetic force
q is the charge of the particle
v is the velocity of the particle
B is the magnetic field strength
θ is the angle between the velocity vector and the magnetic field vector

In this case, both particles have the same velocity and are perpendicular to the magnetic field, so the angle θ is 90 degrees. Therefore, sin(θ) = 1.

For the 3 nC particle with charge q = 3 nC, we can calculate the magnetic force using the given values of B = 2 mT and v.

Next, we need to determine the radius of the circular path followed by the 3 nC particle. We can use the concept of centripetal force to relate the magnetic force to the force required for circular motion:

F = m * (v^2) / r

Where:
F is the magnetic force
m is the mass of the particle
v is the velocity of the particle
r is the radius of the circular path

The mass of the particles is equal, so we can write:

F = (m * v^2) / r

Setting these two equations equal to each other, we can solve for the radius:

(q * v * B) = (m * v^2) / r

Simplifying:

r = (m * v) / (q * B)

Given that the radius of the circular path for the 3 nC particle is 12 cm, or 0.12 m, we can substitute these values into the equation to find the mass of the particles:

0.12 m = (m * v) / (3 nC * 2 mT)

Simplifying:

m = (0.12 m * 3 nC * 2 mT) / v

Now that we have found the mass of the particles, we can calculate the magnetic force on the 3 nC particle using the equation F = q * v * B. Given that the magnetic field B = 2 mT, and the charge q = 3 nC, we can substitute these values into the equation:

F = (3 nC) * v * (2 mT)

Finally, we can calculate the separation between the two particles as they exit the magnetic field. Since both particles exit parallel to each other, the separation will be twice the radius of the circular path followed by the 3 nC particle:

Separation = 2 * r