Physics 202 Homework, Day 07: Chapter 15: #7,9,10
ü 7. Suppose 1.00g of hydrogen is separated into electrons and protons. Suppose that the protons are
placed at the Earth's north pole and the electrons are placed at the South Pole. What is the resulting
compressional force on the earth? (Corrected)
One gram of Hydrogen contains one mole of material, or Avogadro's number of atoms. Each atom contains one electron and
one proton.
In[1]:=
electronCharge = 1.602 * 10-19 ; avogadrosNumber = 6.02 * 1023 ; earthDiameter = 2 * 6.38 * 106 ;
k = 8.99 * 109 ; Force = k
HelectronCharge * avogadrosNumberL2
earthDiameter2
Print@"The compresional force is ", Force, " Newtons."D
;
The compresional force is 513 542. Newtons.
ü 9. Two small identical conducting spheres are placed with their centers 0.30 cm apart. One is given a
charge of 12 x 10-9 C, the other a charge of -18 x 10-9 C.
(a) Find the electrostatic force exerted by one sphere on the other.
(b) The spheres are connected by a conducting wire. Find the electrostatic force between the two spheres
after equilibrium is reached.
(a) The two opposite charges attract each other.
charge1 = 12 * 10-9 ; charge2 = 18 * 10-9 ; r = 0.30 * 10-2 ;
Hcharge1 * charge2L
k = 8.99 * 109 ; Force = k
;
r2
Print@"The attractive force is ", Force, " Newtons."D
The attractive force is 0.21576 Newtons.
(b) When the wire connects the two charges, positive and negative charges neutralize each other, leaving a total charge of - 6
nC. Half of the charges moves to each of the two spheres.
charge1 = 3 * 10-9 ; charge2 = 3 * 10-9 ; r = 0.30 * 10-2 ; k = 8.99 * 109 ; Force = k
Hcharge1 * charge2L
r2
;
Print@"The repulsive force is ", Force, " Newtons."D
The repulsive force is 0.00899 Newtons.
ü 10. Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in the
figure below. (This is really three problems in one... find the vector sum of the forces exerted by the other
two charges on a given charge. Do this three times for the three charges.)
The force on charge 1 is repulsive (-x direction) from charge 2 and attractive (+x direction) from charge 3.
The force on charge 2 is repulsive (+x direction) from charge 1 and attractive (+x direction) from charge 3.
The force on charge 3 is attractive (-x direction) from charge 2 and attractive (-x direction) from charge 1.
2
Day_07_Sol.nb
The force on charge 3 is attractive (-x direction) from charge 2 and attractive (-x direction) from charge 1.
charge1 = 6 * 10-6 ; charge2 = 1.5 * 10-6 ; charge3 = 2.0 * 10-6 ;
r12 = 3.0 * 10-2 ; r23 = 2.0 * 10-2 ; k = 8.99 * 109 ;
Hcharge1 * charge2L
Force12 = k
r122
Hcharge1 * charge3L
Force13 = k
Hr12 + r23L2
Force23 = k
Hcharge2 * charge3L
r232
Print@"The force on charge 1 is ", - Force12 + Force13, " Newtons."D
Print@"The force on charge 2 is ", Force12 + Force23, " Newtons."D
Print@"The force on charge 3 is ", - Force13 - Force23, " Newtons."D
89.9
43.152
67.425
The force on charge 1 is - 46.748 Newtons.
The force on charge 2 is 157.325 Newtons.
The force on charge 3 is - 110.577 Newtons.
Note that these three vector forces add up to 0.