When a beam of cathode rays (or electrons) are subjected to crossed electric (E) and magnetic (B) fields, the beam is not deflected, if  Force on electron due to = Force on electron due magnetic field to electric field Bev = eE or v = E/B  .......(i) If V is the potential difference between the anode and the cathode, then 1/2mv2 = eV e/m = v2/2V .......(ii) Substituting tire value of rt from equation (i) in equation (ii), we get e/m = E2/2VB2 Specific charge of the cathode rays e/m = E2/2VB2

The Specific Charge of Cathode Rays

Cathode rays are streams of electrons that are emitted from the cathode (negative electrode) in a vacuum tube. These rays possess a negative charge and have a high velocity. The specific charge of cathode rays is defined as the ratio of the charge (q) carried by an electron to its mass (m). It is denoted by the symbol (e/m).

Experimental Setup

In this experiment, a beam of cathode rays is subjected to crossed electric and magnetic fields. The electric field is applied perpendicular to the magnetic field, resulting in crossed fields. The strength of these fields is adjusted in such a way that the beam of cathode rays remains undeflected.

Electric Field

The electric field is created by applying a potential difference between two charged plates. The positive plate attracts the negatively charged cathode rays, while the negative plate repels them. The strength of the electric field is controlled by adjusting the potential difference between the plates.

Magnetic Field

The magnetic field is generated by passing an electric current through a coil of wire. The coil is placed perpendicular to the direction of the cathode ray beam. The strength of the magnetic field is controlled by varying the current passing through the coil.

Force on the Cathode Rays

When a charged particle moves through a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field. This force is given by the equation F = qvB, where F is the force, q is the charge, v is the velocity, and B is the magnetic field strength.

In the case of the cathode rays, the force due to the electric field is balanced by the force due to the magnetic field. Since the beam remains undeflected, the electric and magnetic forces are equal in magnitude but opposite in direction. Mathematically, this can be expressed as qE = qvB.

Determination of Specific Charge

By rearranging the equation qE = qvB, we can express the specific charge (e/m) as (e/m) = E/Bv. Here, E represents the electric field strength, B represents the magnetic field strength, and v represents the velocity of the cathode rays.

The electric and magnetic field strengths are adjusted until the cathode ray beam remains undeflected. At this point, the specific charge of the cathode rays can be determined by measuring the values of E, B, and v and plugging them into the equation (e/m) = E/Bv.

Conclusion

The specific charge of cathode rays can be determined by subjecting the beam to crossed electric and magnetic fields and adjusting their strengths to ensure no deflection. By measuring the values of the electric and magnetic field strengths and the velocity of the cathode rays, the specific charge can be calculated using the equation (e/m) = E/Bv. This experiment provides a practical method for determining the specific charge of cathode rays and further understanding the nature of these particles.