# Physics 102, Homework 4

1. Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. At what point between the two wires are the contributions from the two wires the same?

$I_1/2*pi*r_1 = I_2/2*pi*r_2$

$r_1+r_2 = 0.2$

$20*r_2 =5*r_1$

$r_2 = 0.04$, $r_1 =0.16$

C) 0.16 m from the 20 A wire.

2. Starting from rest, a proton falls through a potential difference of 1200 V. What speed does it acquire?

$E_k = mv^2/2$

$V = sqrt{2eU/m} = 480962 m/s$

B) $4.8*10^5 m/s$

3. Estimate the average power output of the Sun, given that about $1350 W/ m^2$ reaches the upper atmosphere of the Earth. The distance from the Sun to the Earth is $1.5 × 10^{11} m$.

$4*pi*r^2*P = 4*pi*(1.5*10^{11})^2* 1350 =3.810^{26} W$

C) $4*10^{26} W$

4. Which of the equations here is valid for the circuit shown?

Clockwise on the left loop.

E) $-2 -I_1 -2*I_2 =0$

5.  An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. What is the angle of refraction in the water for a ray of light that has an angle of incidence of 45° as it enters the oil from the air above? (The index of refraction for oil is 1.15, and for water it is 1.33.)

$sin(i)/sin(r_1) = n(oil) =1.15$

$r_1 = 37.94 deg$

$sin(r_1)/sin(r_2) = n(water)/n(oil) = 1.33/1.15 =1.1565$

$r_2 = 32.11 deg$

B) $32°$

6.  A concave mirror with a radius of 20 cm creates a real image 30 cm from the mirror. What is the object distance?

$1/x_1 + 1/x_2 = 1/f$

f is positive,

$x_1$ is positive is the object is to the left of the mirror

$x_2$ is positive if the image is to the right of the mirror

$f = R/2$

$1/x_1 -1/30 =1/10$

$1/x_1 = 1/10+1/30$

$x_1 = 7.5 cm$

A) $7.5 cm$

7. A point charge of +Q is placed at the centroid of an equilateral triangle. When a second charge of +Q is placed at one of the triangle’s vertices, an electrostatic force of 4.0 N acts on it. What is the magnitude of the force that acts on the center charge due to a third charge of +Q placed at one of the other vertices?

The system is symmetric relative to all 3 vertices.

C) $4.0 N$

8. What current is flowing if $4.0*10^{16}$ electrons pass a point in 0.50 s?

$I = Q/t = n*e/t = 0.0128 A$

D) $0.013 A$

9.  Two charges are separated by a distance d and exert mutual attractive forces of F on each other. If the charges are separated by a distance of d/3, what are the new mutual forces? D) 9F

$F_1 = Q_1*Q_2/D^2$

$F_2 = 9Q_1*Q_2/D^2 = 9*F_1$

C) $9F$

10.  A flux of $4.0*10^{-5} Wb$ is maintained through a coil for $0.50$ s. What emf is induced in this coil by this flux? If the flux is maintained then its variation is zero.

$V_{ind} = -dPhi / dt = 0$

D) No emf is induced in this coil.

only if the flux varies from max to zero in 0.5 sec the induced voltage is

$V_{ind} = -4*10^{-5}/0.5 =8*10^{-5} V$