Electricity 4 Questions

1. For what wavelength of light does a 100 mW laser deliver 2.50 x 1017 photons per second?

2. A long wire carrying a 5.0 A current perpendicular to the (xy)-plane intersects the x-axis at x = -2.00 cm. A second parallel wire carrying a 3.00 A current intersects the x-axis at x = +2.00 cm. At what point or points on the x-axis is the magnetic field zero (a) if the two currents are in the same direction and (b) if the two currents are in opposite directions?

3. 0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20° C. The gas then undergoes isobaric heating to a temperature of 300° C. What is the final pressure of the gas? What is the final volume?

4. What is the electric field strength at x = 0 m, y = 0 m produced by two electrons (one at x = 0.0001 m, y = 0 m and the other at x = -0.0001 m, y = 0 m)? (The value of k is 9.0 x 109 N∙m2/C2) (Points : 5)

2.88 x 10-19 N/C

5.76 x 10-19 N/C

0 N/C

1.8 x 10-19 N/C

1.

Energy $E = h*c/\lambda$   $\lambda$ is the wavelength

Power = total energy/time  $P = n*E/t$

$P*t = n*E = n*h*c/\lambda$

$\lambda = n*h*c/P/t = 2.5*10^{17}*6.62*10^{-34}*3*10^8/0.1/1 =4.965*10^{-7} m =496.5 nm$

2.

The magnetic field of a wire with a current I at distance R is

$B = \mu*I/(2\pi*R)$ , where $\mu$ is the magnetic permeability

when both currents have the same direction the point $x$ is between the two wires

$I1/R1 = I2/R2$,   $R1/R2 = I1/I2$
$R1+R2 = 4$ cm

$R2*(I1/I2) +R2 = 4$ cm

$R2*5/3 +R2 = 4$ cm

$8/3 * R2 = 4$ cm

$R2 = 12/8 = 1.5$ cm left to the left wire, it means at $x = +0.5$ cm

when currents are opposite the point $x$ is to the right of the second wire (3 A)

$I1/R1 = I2/R2$

$R1-R2 =4$ cm

$R2*5/3 -R2 =4$ cm

$2/3 * R2 = 4$ cm

$R2 = 12/2 = 6$ cm to the right of the second wire it means at $x =2+6 =8$ cm

3.

$P*V = \nu*R*T$ where $\nu$ is the number of moles

Isobaric heating means the pressure remains the same. The final pressure is

$P = \nu*R*T/V =0.1*8.314*(20+273)/50*10^{-6} =4.872*10^6 (N/m^2)$

The final volume comes from

$V1/T1 = V2/T2$  where T is the absolute temperature

$V2 = V1*T2/T1 = 50*10^{-6} *(273+300)/(273+20) =324.2*10^{-6} m^3 = 324.2 cm^3$

4.

The field of a charge is in absolute value

$E = k*q/R^2$ where $k =9*10^9$

since it is a vector the lines of field exits the positive charges and enters the negative charges. Since both electrons have negative charges the two vectors representing the electric field are opposite and equal hence the total field at x = 0 is zero. Correct answer is C) 0 N/C