NTA Abhyas 2020
- Exam
- NTA Abhyas
- Year
- 2020
- Subject
- Physics
- Chapter
- Magnetic Properties of Matter
NTA Abhyas 2020 · Physics · Magnetic Properties of Matter
A thin spherical shell of radius R is cut into two equal halves and...
A thin spherical shell of radius is cut into two equal halves and then each of its halves is charged to the same uniform surface charge density . If is the force exerted on each half to keep them at equilibrium, then & is& proportional to
Options
- A\dfrac{1}{{ε}_{0}} {σ}^{2} \text{R}
- B\dfrac{1}{{ε}_{0}} \dfrac{{σ}^{2}}{\text{R}}
- C\dfrac{1}{{ε}_{0}} \dfrac{{σ}^{2}}{R^{2}}
- D\dfrac{1}{{ε}_{0}} {σ}^{2} R^{2}
Correct answer
D. \dfrac{1}{{ε}_{0}} {σ}^{2} R^{2}
Step-by-step solution
Electrical force per unit area = \dfrac{1}{2} {ε}_{0} E^{2} = \dfrac{1}{2} {ε}_{0} {\left(\dfrac{σ}{{ε}_{0}}\right)}^{2} = \dfrac{{σ}^{2}}{2 {ε}_{0}}
Projected area = π R^{2}
∴ Net electrical force = \left(\dfrac{{σ}^{2}}{2 {ε}_{0}}\right) \left(π R^{2}\right)∴\text{F} = \dfrac{π {σ}^{2} R^{2}}{2 {ε}_{0}}\text{F} ∝ \dfrac{{σ}^{2} R^{2}}{{ε}_{0}}
Projected area = π R^{2}
∴ Net electrical force = \left(\dfrac{{σ}^{2}}{2 {ε}_{0}}\right) \left(π R^{2}\right)∴\text{F} = \dfrac{π {σ}^{2} R^{2}}{2 {ε}_{0}}\text{F} ∝ \dfrac{{σ}^{2} R^{2}}{{ε}_{0}}