A disk of radius R with uniform positive surface charge density σ lies in the xy-plane with centre at the origin. The potential on the z-axis is V(z) = [σ/(2ε₀)](√(R² + z²) - z). A positive charge q starts from rest at z = z₀ > 0. In addition to the Coulomb force it experiences a constant force $\vec{F}$ = -c $\hat{k}$ , c > 0. Define β = 2cε₀/(qσ). Which statement(s) is/are correct?
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Question

A disk of radius R with uniform positive surface charge density σ lies in the xy-plane with centre at the origin. The potential on the z-axis is V(z) = [σ/(2ε₀)](√(R² + z²) - z). A positive charge q starts from rest at z = z₀ > 0. In addition to the Coulomb force it experiences a constant force $\vec{F}$ = -c $\hat{k}$ , c > 0. Define β = 2cε₀/(qσ). Which statement(s) is/are correct?

Select all that apply

G1 Physics · Accepted Answer

Step 1: Write total potential energy U(z)=qV(z)+cz and divide by qσ/(2ε₀); the dimensionless energy is u(z)=√(R²+z²)+(β-1)z. Step 2: Motion from rest is allowed wherever U(z)≤U(z₀); turning points satisfy equality. Step 3: Testing the stated β,z₀ values gives A and C, and for β>1 the total potential rises with z so a particle released at z₀ always moves toward the origin. Final: A, C, D.