A spark passes though air when the potential gradient is `3xx10^(6) `volts per metre what must be the radious of an isoated metal sphere which can be changed to a potentiial of 3 million voilts before there are sparks in the air?

The existence of negatively charged particle in an atom was shown by J.J. Thomson as a result of the studies of the passage of electricity through gases at extremely low pressure known as discharge tube experiments. When a high voltage of the order of 10,000 volts or more was impressed across the electrodes, some sort of invisible rays moved from the negative electrode to the positive electrode these rays are called as cathode rays. Cathode rays travel in straight path in absence of electrical and magnetic field . Cathode rays consist of material part and charged particles? Cathode rays produce X-rays and light is emitted when they strike on ZnS screen. Cathode rays penetrate through thin sheets of aluminium and other metals . They affect the photogenic plate and passes heating effect when they strike on metal foil. The raito of charge to mass i.e charge/mass is same for all the cathode rays irrespective of the gas used in the tube. The existence of positively charged particle in an atom was shown be E. Goldstein. He repeated the same discharge tube experiments by using a perforated cathode. It was observed that when a high potential difference was applied between the electrodes, not only cathode rays were produced but also a new type of rays were produced simultaneoulsy from anode moving towards cathode and passes through the holes or canal of the cathode. These termed as canal rays or anode rays. These rays travel in straight lines and consists of positively charged particles. These rays have kinetic energy and produces heating effect also. The e/m ratio of these rays is smaller than that of electrons. Unlike cathode rays, their e/m value is dependent upon the nature of the gas taken in the tube. These rays produced flashes of light on ZnS screen and can pass throughs thin metal foils. They can produce physical and chemical changes and are capable to produce ionisation in gases. Which is not true with respect to cathode rays?

Dielectric strength of air is 3xx10^6 V m^-1 . If electric potential on a sphere can be 9xx10^6V , then find the minimum radius of the sphere.