12. What is the relationship between the power P emitted by a blackbody and its temperature T?
(A) P ∝ T
(B) P ∝ T²
(C) P ∝ T³
(D) P ∝ T⁴
(E) P ∝ T⁵

8. Four point charges of +0.500 μC, +1.50 μC, -1.00 μC, and -0.500 μC are randomly distributed on a ring. If the electric potential at the center of the ring due to the +0.500 μC charge alone is 4.5 × 10⁴ V, what is the total electric potential at the center due to all four charges?(A) 0(B) -4.5 × 10⁴ V(C) 4.5 × 10⁴ V(D) 9.0 × 10⁴ V(E) 18.0 × 10⁴ V

9. A charged particle with mass m and charge q enters a magnetic field B at angle θ with velocity v. What is the radius of the helical trajectory? (A) mv/(qB) (B) mvsinθ/(qB) (C) mvcosθ/(qB) (D) qB/(mv) (E) λ/(2π)

10. An infinitely large, thin conducting sheet carries a uniform current density J. What is the magnetic field at a distance r perpendicular to the surface of the sheet? (A) 1/2 μ0 J (B) 1/2 μ0 Jr (C) μ0 J (D) μ0 Jr (E) 1/2 μ0 J2

11. The magnetic flux varies with time as Φ(t) = Φ₀e⁻ᵇᵗ. What is the maximum induced emf? (A) bΦ₀ (B) Φ₀/b (C) 0 (D) Φ₀²b (E) Φ₀/b²

13. In the photoelectric effect, which equation relates stopping voltage U₀ and wavelength λ? (A) hc/(eλ) = U₀ (B) eU₀ = hc/λ (C) U₀ = hc /(eλ) – φ (D) U₀ = φ – hc /(eλ) (E) φ = U₀

14. In a hydrogen atom, what is the energy difference between n = 3 and n = 2? (A) 13.6 eV (B) 1.89 eV (C) 3.4 eV (D) 10.2 eV (E) 12.1 eV

15. An observer measures a clock moving at speed v = 0.6c. What is the time dilation factor γ? (A) 1.0 (B) 1.15 (C) 1.25 (D) 1.50 (E) 2.0

16. What is the energy density ratio of electric and magnetic fields in an electromagnetic wave? (A) Equal (B) Electric is twice magnetic (C) Magnetic is twice electric (D) Cannot be compared (E) Depends on frequency

17. A radio station requires a coaxial cable to connect the transmitter to the antenna. The cable consists of an inner conductor with a diameter of 0.2 mm and an outer conductor with a diameter of 2.0 mm, whose thickness is negligible. If the maximum safe potential difference between the conductors is 2.3 kV, what is the maximum charge density the conductors can carry under this safety constraint? (A) 45 μC (B) 50 μC (C) 55 μC (D) 60μC (E) 65 μC

18. A spreading wave packet increases in width over time due to which principle? (A) Second Law of Thermodynamics (B) Conservation of Energy (C) Relativistic Effect (D) Uncertainty Principle (E) Momentum Conservation