A charged particle, attached to a string fixed at one point, is...

Initially, the tension in the string provides the necessary centripetal force for the circular motion of the charged particle. Let the mass of the particle be $m$, its speed be $v$, and the radius of the circle be $r$. The initial tension is given by:

$T_{0} = \dfrac{mv^2}{r}$

When a vertical magnetic field $\vec{B}$ is switched on, a magnetic Lorentz force $\vec{F}_{m} = q(\vec{v} \times \vec{B})$ acts on the particle. Since the velocity $\vec{v}$ is in the horizontal plane and $\vec{B}$ is vertical, the magnetic force will act along the radial direction (either towards the center or away from the center).

Depending on the sign of the charge $q$, the direction of the velocity $\vec{v}$, and the direction of the magnetic field $\vec{B}$, the magnetic force $F_{m} = qvB$ can be directed radially inward or radially outward.

If $\vec{F}_{m}$ is directed radially inward, the new tension $T$ is:

$T + F_{m} = \dfrac{mv^2}{r} \Rightarrow T = \dfrac{mv^2}{r} - F_{m}$ (Tension decreases)

If $\vec{F}_{m}$ is directed radially outward, the new tension $T$ is:

$T - F_{m} = \dfrac{mv^2}{r} \Rightarrow T = \dfrac{mv^2}{r} + F_{m}$ (Tension increases)

Since the specific directions and the sign of the charge are not provided, the tension in the string may increase or decrease.