Two insulated charged metallic spheres P and Q have their centres sepa...
Here, q
1 = q
2 = 3.2 x 10
-7 C, r = 60cm = 0.6 m
Electrostatic force,
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Two insulated charged metallic spheres P and Q have their centres sepa...
The mutual force of electrostatic repulsion between two charged metallic spheres
Given:
- Two insulated metallic spheres P and Q.
- The centres of P and Q are separated by a distance of 60 cm.
- The radii of P and Q are negligible compared to the distance of separation.
- The charge on each sphere is 3.2 x 10^-7 C.
To find:
- The mutual force of electrostatic repulsion between the two spheres.
Explanation:
Step 1: Calculating the electric field
- The electric field between two charged spheres can be calculated using the formula:
E = k * (Q / r^2)
where E is the electric field, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), Q is the charge on the sphere, and r is the distance between the centres of the spheres.
- Substituting the given values, we get:
E = (9 x 10^9 Nm^2/C^2) * (3.2 x 10^-7 C) / (0.6 m)^2
E = 2.133 x 10^4 N/C
Step 2: Calculating the force of repulsion
- The force of repulsion between two charged spheres can be calculated using the formula:
F = Q * E
where F is the force of repulsion, Q is the charge on each sphere, and E is the electric field.
- Substituting the given values, we get:
F = (3.2 x 10^-7 C) * (2.133 x 10^4 N/C)
F = 6.826 x 10^-3 N
- Converting the force to scientific notation, we get:
F = 6.826 x 10^-3 N
F = 6.826 x 10^-3 N
F ≈ 6.83 x 10^-3 N
Step 3: Rounding the answer
- Rounding the answer to the nearest significant figure, we get:
F ≈ 6.8 x 10^-3 N
Final Answer:
The mutual force of electrostatic repulsion between the two spheres is approximately 6.8 x 10^-3 N, which is equivalent to option B.
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