Question

The Stanford Linear Accelerator accelerated a beam consisting of 2.6 times 10^14 electrons per second through a potential difference of 2.6 10^10 V. Calculate the current in the beam. Calculate the power of the beam. Calculate the effective ohmic resistance of the accelerator {4.17 times 10^-05 A, 1.08 times 10^+06 W, 6.24 times 10^+14 ohm}

Answer 1

a )

given

dq = 2.6 X 10¹⁴ electrons

dq = 2.6 X 10¹⁴ X 1.6 X 10^-19

per second means t = 1 sec or dt = 1 sec

so to get current value using equation

i = dq / dt

i = 2.6 X 10¹⁴ X 1.6 X 10^-19 / 1

i = 4.16 X 10^-5 amp

the current is i = 4.16 X 10^-5 amp

b )

given

V = 2.6 X 10¹⁰ volts

using the equation for the power is " P "

P = V X i

P = 2.6 X 10¹⁰ X 4.16 X 10^-5

P = 1081600 W

P = 1.081600 X 10⁶ W

the power of the beam is P = 1081600 W

c )

using the equation to get resistance value is

using ohm's law V = i X R

R = V / i

R = 2.6 X 10¹⁰ / 4.16 X 10^-5

R = 6.25 X 10¹⁴ $\Omega$

the resistamce is R = 6.25 X 10¹⁴ $\Omega$