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Chapter 26: Problem 19

A velocity selector uses a 60 -mT magnetic field perpendicular to a 24 -kN/C electric field. At what speed will charged particles pass through the selector undeflected?

Short Answer

Expert verified
The speed at which charged particles will pass through the selector undeflected is 400,000 m/s.

Step by step solution

01

Understand the Forces at Play

In a velocity selector, a charged particle is subject to both an electric force (equal to the charge multiplied by the electric field strength, or \(F_e = qE\)) and a magnetic force (equal to the charge multiplied by the product of the velocity and the magnetic field strength, or \( F_b = qvB\)). If the particle is passing undeflected, that means these two forces must be exactly counteracting each other. So, \(F_e = F_b\).
02

Solve the Equations

By setting the two forces equal to each other, \(qvB = qE\), the charge (\(q\)) cancels out and you are left with a simple equation for the velocity (\(v\)): \(v = E / B\).
03

Substitute the Given Values

Substitute the given values for the electric field (\(E = 24 kN/C = 24 * 10^3 N/C\)) and the magnetic field (\(B = 60mT = 60 * 10^{-3} T\)) into the formula. The result is \(v = 24 * 10^3 / (60 * 10^{-3}) = 400,000 m/s.\)

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