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Calculate the magnitude of the force

F on the charge q given that the square is

10.70 cm on a side and q=2.15μC

.

Calculate the magnitude of the force F on the charge q given that the square is 1070 cm on a side and q215μC class=

Respuesta :

bhuvna789456

The magnitude of the force F on a charge is 3.633 N.

Explanation:

  • The magnitude of the force on a charge can be found by using the Coulombs law which states that between two charged objects, the magnitude of electric force is directly proportional to the charge on each object.
  • The magnitude of force in a charge is a point charge with a magnitude q, at a point of distance away from the point charge and the formula for the magnitude of force on a charge is given as

                            F = (k * q1q2) / r^2

where k is constant value = 9 * 10^9,

           q is the point charge(q1 = q2),

            r is the distance = 10.70 cm = 0.107 m.

magnitude of force on a charge = (9 * 10^9) (2.15 * 10^-6)^2 / (0.107)^2

                                                      = 3.633 N.

pristina

From Coulomb's law, symmetry of arrangement and polarity of charges we can find that the total force on q is directed downwards. The magnitude of force on charge q is 77.084 N.

Given that q is a positive charge.

  • Force on q due to [tex]q_a[/tex] will be repulsive, as [tex]q_a[/tex] is also positive. This force is directed away from [tex]q_a[/tex], ie; towards [tex]q_d[/tex] or towards bottom right (as [tex]q_d[/tex] is diagonally opposite to [tex]q_a[/tex]).
  • Similarly, the force on q due to [tex]q_b[/tex] will also be repulsive. This force is away from [tex]q_b[/tex], that means towards [tex]q_c[/tex] or bottom left.
  • Force on q due to [tex]q_c[/tex] will be attractive, as [tex]q_c[/tex] is negative. This force is directed towards bottom right.
  • Similarly, the force on q due to [tex]q_d[/tex] will also be attractive. This force is directed towards [tex]q_d[/tex] or bottom left.
  • So there will be forces of equal magnitudes directed towards the bottom right and bottom left. Therefore the resultant force will be directed straight down.

Now to find the magnitude of the force. We just have to find the y-component of all the four forces. Since the x-components cancels away, only the y-components will be left.

  • Since all charges have equal magnitude; we can find the force on q due to any one charge. Find the y-component of the force and multiply it by 4.
  • From Coulomb's law we can have magnitude of force;
  • [tex]F = k\frac{|q_1 q_2 |}{r^2}[/tex]

But r can be found out using the Pythagoras theorem.

[tex]r=\sqrt{5.35^2 +5.35^2} = 7.566\,cm=0.0756\,m[/tex]

First we find force due to [tex]q_a[/tex];

[tex]F_a = k\frac{|q_a \times q |}{r^2}[/tex]

So, [tex]F=(9\times 10^9\,Nm^2/C^2)\frac{(8.05\times 10^{-6}\,C) \times (2.15\times 10^{-6}\,C)}{(0.0756m)^2}[/tex]

[tex]F_a=27.254\, N[/tex]

Now to find the y component of the force;

[tex]F_{ay}= F_a \,cos\,45^{o} =27.254 \times \frac{1}{\sqrt{2} }= 19.271\, N[/tex]

Therefore, total force[tex]F_y=F_{ay}+F_{by}+F_{cy}+F_{dy}[/tex]

But; [tex]F_{ay}=F_{by}=F_{cy}=F_{dy}[/tex]

Therefore magnitude of total force on q,

[tex]F_y = 4\times F_{ay} = 4\times 19.271 \,N = 77.084 N[/tex]

Therefore the magnitude of total force on q is 77.084 N.

Learn more about Coulomb's Law here:

https://brainly.com/question/14699719

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