Two charges of # -7 C # and # 4 C # are at points # (4, 7 ,-8) # and # ( -1 , 3, -8 )#, respectively. Assuming that both coordinates are in meters, what is the force between the two points?

Question

Two charges of #  -7 C # and #  4  C # are at points #  (4, 7 ,-8)  #  and #  (  -1  ,  3,  -8  )#, respectively.  Assuming that both coordinates are in meters, what is the force between the two points?

HIX Tutor · Accepted Answer

undefined To find the force between the two charges, we can use Coulomb's Law formula:

1. Calculate the distance between the two points using the distance formula: 
Distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]

2. Substitute the values into Coulomb's Law formula: 
Force = (k * |q1 * q2|) / Distance^2
where k is Coulomb's constant (8.99 x 10^9 N m^2/C^2) and q1, q2 are the charges given.

3. Plug in the values for distance, charges, and Coulomb's constant to calculate the force.

Emily Abbate · Answer

The force is #-0.25*10^12# N.

The force of Coulomb is #F=1/(4pi epsilon_0)(Q_1 Q_2)/r^2#. The only unknown quantity is #r#, the distance between the two charges. We can calculate using the Pitagora's theorem in three dimensions: #r=sqrt((x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2)=sqrt((4+1)^2+(7-3)^2+(-8+8)^2)= sqrt(5^2+4^2+0^2)=sqrt(5^2+4^2+0^2)=sqrt(41)#. The power is #F=1/(4pi epsilon_0)(Q_1 Q_2)/r^2=1/(4*3.14*8.854*10^-12)*((-7)*4)/(41)=-(28*10^12)/(4*3.14*8.854)=# #-(28*10^12)/111.20624=-0.25*10^12# N. The minus sign means that the two charges are attracting each other.

Isabella Alvarez · Answer

undefined The force between the two charges is approximately $8.39 \times 10^{10}$ Newtons.