Question

Scientists are working on a new technique to kill cancer cells by zapping them with ultrahigh-energy (in the range of 1012 W) pulses of electromagnetic waves that last for an extremely short time (a few nanoseconds). These short pulses scramble the interior of a cell without causing it to explode, as long pulses would do. We can model a typical such cell as a disk 5.6 μm in diameter, with the pulse lasting for 3.0 ns with an average power of 2.47×1012 W . We shall assume that the energy is spread uniformly over the faces of 100 cells for each pulse.

Part A: How much energy is given to the cell during this pulse?

Part B: What is the intensity (in W/m2) delivered to the cell?

Part C: What is the maximum value of the electric field in the pulse?

Part D: What is the maximum value of the magnetic field in the pulse?

Answer 1

Part A.

Energy given to the cell during this pulse will be:

E = P*t

t = time interval of pulse = 3.0 ns = 3.0*10^-9 sec

E = 2.47*10^12*3.0*10^-9

E = 7410 J

Since this energy is spread uniformly over the faces of 100 cells of each pulse, So

E0 = energy given to each pulse = E/100 = 7410/100 = 74.1 J

In two significant figures E0 = 74 J

Part B.

Relation between intensity and Power is given by:

Intensity = Power/Area = P/A = P/(pi*r^2)

Now Intensity delivered to each cell will be:

I = P/(100*pi*r^2)

r = radius of each cell = 5.6*10^-6 m/2 = 2.8*10^-6 m

So,

I = 2.47*10^12/(100*pi*(2.8*10^-6)^2)

I = 1.0*10^21 W/m^2

Part C.

relation between intensity and electric field is given by:

I = (1/2)*c*e0*E_max^2

E_max = sqrt (2*I/(c*e0))

E_max = sqrt (2*1.0*10^21/(3*10^8*8.85*10^-12))

In two significant figures:

E_max = 8.7*10^11 N/C

Part D.

Relation between electric field and magnetic field is given by:

B_max = E_max/c

B_max = 8.7*10^11/(3*10^8)

B_max = 2900 T = 2.9*10^3 T

Let me know if you've any query.