Dentists use x-rays to image their patients’ teeth and bone. The x-ray tubes tha

Question

Dentists use x-rays to image their patients’ teeth and bone. The x-ray tubes that generate x-rays contain an electron source separated by about 10cm from a metallic targets. The electrons are accelerated from the source to the target by a uniform electric field with a magnitude of about 100kN/C , as drawn in the figure above. When the electrons hit the target, x-rays are produced. (a) What is the potential difference between the electron source and the metallic target? (b) What is the kinetic energy of the electrons when they reach the target (assume that the electrons start at rest)?

Explanation / Answer

(a) Electric field = 100 kN/C = 100000 N/C

Other unit of electric field is V/m.

So, electric field can also be written as -

E = 100000 V/m

Now the distance between the source and the metallic target, d = 10 cm = 0.10 m

So, the requisite potential difference between source and the metallic target, V = E*d

= 100000 * 0.10 = 10000 V = 10 kV.

(b) Charge of an electron, q = 1.6 x 10^-19 C

So, kinetic energy of an electron when it reaches at the target = q*V = 1.6 x 10^-19 x 10000 = 1.6 x 10^-15 J

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