An oscillating electric dipole of moment d (t) = d0 cos(𝜔t) ẑ is placed at origin as
shown in figure.
Consider a point P(r, 𝜃, 𝜙) at a very large distance from the dipole. Here r, 𝜃 and
𝜙 are spherical polar coordinates. Which of the following statement is/are true for
intensity of radiation?
Options:
(A) Intensity is zero if P is on the z axis
(B) Intensity is zero at P (r = R, 𝜃 =
𝜋
2 , 𝜙 =
𝜋
4)
(C) Intensity at P (r = R, 𝜃 =
𝜋
2 , 𝜙 =
𝜋
4) is greater than that
at P (r = R, 𝜃 =
𝜋
4 , 𝜙 =
𝜋
4)
(D) Intensity at P (r = R, 𝜃 =
𝜋
2 , 𝜙 =
𝜋
4) is equal to that at P (r = R, 𝜃 =
𝜋
4 , 𝜙 =
𝜋
4)
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2024 Q.55)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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