Question

5) In the device diagrammed below an accelerator injects a beam of positively charged ions into the evacuated space between two metal plates. The ions are assumed to be missing one electron and they all seem to leave the accelerator with the same speed. A uniform magnetic field of magnitude 0.1 T is maintained between the plates. In separate experiments beams of ions are injected into the space between the plates . In the first experiment the beam of ions ("ion beam 1" below) interacts with the magnetic field and the particles follow a circular trajectory of radius 15.3 cm as shown. a) In which direction is the magnetic field directed? Briefly explain how you know. b) In the second experiment, with the magnetic field present as before, the scientists decide to use an electric field to make the particles follow a straight path, and so they apply a voltage across the plates. They find that when the uniform electric field has a magnitude of 4.2 x 10' V/m -4.2 x 10 N/C (this takes a number of trials) a second ion beam ("ion beam 2" below) will travel straight through without deflection. Assuming both ion beams are composed of the same type of ions and (as stated above) all leave the

Answer 1

Magnetic field strength is B = 0.1 T Charge of the ion is q = 1.6 times 10^-19 c. Let v be the speed of the ion and m be the mass of the ion. Force on the ion due to magnetic field is F^vector_m = q middot v^vector times B^vector direction of force will be same as the direction of v^vector times B^vector from the figure \r\n from right hand thumbrule direction of magnetic field will be into the page. Force on the particle due to electric field is F^vector_e = q E^vector direction of F^vector_e will be same as direction of E^vector. Since path of the ion is straight so net force on the ion will be zero. That is electric force on the ion should we downward to balance the magnetic force. That is direction of electric field will be downward. Free body diagram of the ion is Since ion is undeflected so net force on the