Question

A doubly ionized molecule (i.e., a molecule lacking two electrons), moving in a magnetic field, experiences a magnetic force of 6.71 × 10⁻¹⁶ N as it moves at 371 m/s at 79.7° to the direction of the field. Find the magnitude of the magnetic field.

Answer 1

To find the magnitude of the magnetic field, we need to rearrange the formula for the magnetic force experienced by a charged particle moving in a magnetic field. By substituting the given values, we can solve for the magnitude of the magnetic field.

Step-by-step explanation:

To find the magnitude of the magnetic field, we can use the formula for the magnetic force experienced by a charged particle moving in a magnetic field,

F = |q|(v⨯B)

where F is the magnetic force, q is the charge of the particle, v is its velocity, and B is the magnetic field strength.

In this case, the force is given as 6.71 × 10⁻¹⁶ N, and the velocity of the molecule is 371 m/s at an angle of 79.7° to the direction of the magnetic field. The charge of the molecule can be determined by rearranging the equation:

|q| = F / (v⨯B)

By substituting the given values and solving for |q|, we can then find the magnitude of the magnetic field B by rearranging the original equation:

B = F / (|q|⨯v)

Substituting the known values, we can find the magnitude of the magnetic field:

B = 6.71 × 10⁻¹⁶ N / (|q|⨯371 m/s)