Problem #0158 Electricity & Magnetism Sub-menu Problem #0160 Chapters Chapters


Problem 29.13P (HRW)

An ion source is producing , each with a charge of . The ions are accelerated by a potential difference of 10 kV and pass horizontally in a region in which there is uniform magnetic field of magnitude . We have to calculate the strength of the smallest electric field, to be set up over the same region, which will allow the ions to pass through undeflected.

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We will first determine the velocity that a ion have after being accelerated by a 10 kV potential difference. Let us assume that the speed acquired is non-relativistic. That is

Mass of a ion will be

Kinetic energy of a ion of charge +e after falling across a potential difference of 10 kV will be

Velocity of ion, when it enters the region where uniform electric and magnetic fields perpendicular to the velocity vector of the charged ion and orthogonal to each other, will be

For ions to go through undeflected in the region of uniform electric and magnetic fields the condition to be fulfilled is


Magnetic field through which the ions move is

Therefore, the electric field has to be