You\'ve just learned about the earth\'s magnetic field and how a compass works a

Question

You've just learned about the earth's magnetic field and how a compass works and you are relaxing in front of the TV. Tired of your show, you think about how the picture tube works in relation to what you have learned. In a typical color picture tube for a TV, the electrons are boiled off of a cathode at the back of the tube and are accelerated through about 20,000 volts towards the picture tube screen. On the screen is a grid of "color dots" about 1/100 inch apart. When the electrons hit them, the dots scintillate their appropriate colors producing the color picture. Without taking apart the set, you determine whether the manufacturer needed to shield the color picture tube from the earth's magnetic field? (earth's B field varies from 0.3 to 0.6 gauss (1 gauss = 10^-4T)

Explanation / Answer

the change in position is,

    dx = (1/2)at^2

        = (1/2)(qvB/m)(L/v)     [since, v = L/t and ma = qvB]

        = (1/2)(qBL^2 / mv)     [since, v = sqrt[2mK]]

Then the change in position is,

    dx = (1/2)(qBL^2 / m[sqrt[2mK]])

        = (1/2)(qBL^2 / m[sqrt[2mqV]])      [since, K= qV]

Here, q = 1.6x10-19, B = 0.3x10-4, L = 0.5 (Take this value for large maximize TV), V = 20,000, m = 9.11x10-31

so, the required result is,

    dx = 0.0078578 m = 0.008 m = 0.3 inch

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