A charged particle of mass m and charge q, having passed the potential difference U, flies into a flat capacitor

A charged particle of mass m and charge q, having passed the potential difference U, flies into a flat capacitor parallel to its plates. Distance between plates d, potential difference Δφ. The capacitor is in a uniform magnetic field. What must be the induction B of the magnetic field so that the particle speed does not change?

The particle moves in a straight line both in a magnetic field and in an electric one:

Fl = Fel;
Fl = q * V * B;
Fel = q * E;
V * B = E (E = Δφ / d);
Let’s find the speed of a given particle after its acceleration:
(m * V ^ 2) / 2 = q * U;
V = √ (2 * q * U) / m – particle velocity;

B = E / V = (Δφ / d) * √ (2 * q * U) / m;

Answer: (Δφ / d) * √ (2 * q * U) / m.