Two 10-cm-diameter charged rings face each other, 20cm apart. The left ring is charged to -22nC and the right ring is charged to +22nC .
What is the magnitude of the electric field E⃗ at the midpoint between the two rings?
To find the magnitude of the electric field (E) at the midpoint between the two rings, we can use the principle of superposition. This principle states that the total electric field at a given point is the vector sum of the electric fields created by each charged object.
In this case, the two rings have opposite charges, and we need to calculate the electric field at the midpoint between them.
Step 1: Calculate the electric field due to the left ring:
The electric field (E1) due to a charged ring at a point on its axial line can be calculated using the formula:
E1 = k * Q1 / R^2
Where:
k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2)
Q1 is the charge on the ring (in this case, -22nC, which is -22 x 10^-9 C)
R is the radius of the ring (10 cm, which is 0.1 m)
Plugging in the values, we get:
E1 = (8.99 x 10^9 Nm^2/C^2) * (-22 x 10^-9 C) / (0.1 m)^2
Step 2: Calculate the electric field due to the right ring:
The electric field (E2) due to the right ring is the same as the electric field due to the left ring, but with the opposite sign because the charges have opposite signs.
E2 = -E1
Step 3: Calculate the net electric field at the midpoint:
The net electric field (E_net) at the midpoint between the two rings is the vector sum of the electric fields due to each ring. Since the rings are aligned on the same axis, the two electric fields are in the same direction, so we can simply add their magnitudes.
E_net = E1 + E2
Now, we can substitute the value of E2 from step 2 into the equation:
E_net = E1 - E1 = 0
Therefore, the magnitude of the electric field at the midpoint between the two rings is zero.
To find the magnitude of the electric field at the midpoint between the two rings, we can use the principle of superposition. We need to consider the electric field due to each ring separately and then add them vectorially.
Let's denote the midpoint between the two rings as point P.
1. Electric field due to the left ring:
The electric field at point P due to the left ring can be calculated using the formula for the electric field of a charged ring.
Electric field due to a ring = (1 / 4πε₀) * (Q / r²),
where ε₀ is the permittivity of free space, Q is the charge on the ring, and r is the distance from the ring to the point where the electric field is being calculated.
Given:
Charge on the left ring = -22 nC = -22 * 10⁻⁹ C
Diameter of the ring = 10 cm = 0.1 m
Radius of the ring = 0.05 m
Distance from the left ring to point P = 10 cm = 0.1 m
Electric field due to the left ring = (1 / 4πε₀) * ((-22 * 10⁻⁹ C) / (0.1 m)²)
2. Electric field due to the right ring:
The electric field at point P due to the right ring will have the same magnitude as the electric field due to the left ring, as the charges on both rings are equal in magnitude. However, the direction will be opposite.
3. Vector addition of the electric fields:
To find the net electric field at point P, we need to vectorially add the electric fields due to the left and right rings. Since the magnitudes are the same and the directions are opposite, the net electric field will be zero.
Therefore, the magnitude of the electric field at the midpoint between the two rings is 0.
try
C(x) = 4.00 + 0.40⌈10x⌉