Respuesta :
Answer:
A) E = 0N/C
B) 0i + 0^^j
C) F = 0N
D) 0^i + 0^j
Explanation:
You assume that the rings are in the zy plane but in different positions.
Furthermore, you can consider that the origin of coordinates is at the midway between the rings.
A) In order to calculate the magnitude of the electric field at the middle of the rings, you take into account that the electric field produced by each ring at the origin is opposite to each other and parallel to the x axis.
You use the following formula for the electric field produced by a charge ring at a perpendicular distance of r:
[tex]E=k\frac{rQ}{(r+R^2)^{3/2}}[/tex] (1)
k: Coulomb's constant = 8.98*10^9Nm^2/C
Q: charge of the ring
r: perpendicular distance to the center of the ring
R: radius of the ring
You use the equation (1) to calculate the net electric field at the midpoint between the rings:
[tex]E=k\frac{rQ}{(r^2+R^2)^{3/2}}-k\frac{rQ}{(r^2+R^2)^{3/2}}=0\frac{N}{C}[/tex]
The electric field produced by each ring has the same magnitude but opposite direction, then, the net electric field is zero.
B) The direction of the electric field is 0^i + 0^j
C) The magnitude of the force on a proton at the midpoint between the rings is:
[tex]F=qE=q(0N/C)=0N[/tex]
D) The direction of the force is 0^i + 0^j
Part A: The magnitude of the electric field generated at the midpoint between two rings is equal that is 0 N/C.
Part B: The direction of the electric field at the midpoint is opposite.
Part C: The magnitude of the force generated on a proton at the midpoint between two rings is equal that is 0 N.
Part D: The direction of the force on a proton at the midpoint is opposite.
Electric field
An electric field is defined as the region that surrounds electrically charged particles and exerts a force on all other charged particles within the region, either attracting or repelling them.
Given that diameter of the ring is 10 m and they are 25 m apart from each other. The charge on the left ring is -25nC and on the right ring is 25nC. The electric field can be given as below.
[tex]E = \dfrac {kQ}{(r+R)^2}\\ [/tex]
Where Q is the charge, r is the radius of the ring, R is the mid-point distance and k is the constant.
Part A
The electric field at the mid-point will be the sum of the electric field generated by both the rings. Substituting the values in the above equation,
[tex]E = \dfrac {8.9\times 10^9\times 25}{(10 +12.5)^2}+\dfrac {8.9\times 10^9\times (-25)}{(10 +12.5)^2}[/tex]
[tex]E = \dfrac {222.5\times 10^9}{506.25} - \dfrac {222.5\times 10^9}{506.25}\\ [/tex]
[tex]E = 0\;\rm N/C[/tex]
Hence we can conclude that both the rings generate the electric field with the same magnitude but they are opposite in direction.
Part B
The electric field at the mid-point is 0 N/C. In the vector form, the electric field can be given as below.
[tex]E = 0i+0j[/tex]
The vector form shows that the electric field at the mid-point between the two rings has the same magnitude but is opposite in direction.
Part C
The force can be given as below.
[tex]F = qE[/tex]
[tex]F = 0 \;\rm N[/tex]
If the electric field at the mid-point is zero, then the force at the mid-point will be zero.
Part D
The vector form of the force at the midpoint is given below.
[tex]F = 0i+0j[/tex]
Hence we can conclude that at the midpoint of two rings, the electric field generates an equal force on the proton but in opposite direction. Hence the net force will be zero.
To know more about the electric field, follow the link given below.
https://brainly.com/question/4440057.
