Step-by-step Solution

To determine which field pattern is valid for both electric and magnetic fields, we must analyze the fundamental properties of electric and magnetic field lines.

1. Properties of Electric Field Lines

• Sources and Sinks: Electric field lines originate from positive charges and terminate on negative charges (or at infinity). This is a consequence of Gauss's law for electricity, $\oint \vec{E} \cdot d\vec{A} = \frac{q_{enc}}{\epsilon_0}$. This means electric fields can have sources and sinks.
• Conservative Nature (Electrostatics): Electrostatic field lines can never form closed loops. This is because the electrostatic field is conservative, meaning the work done in moving a charge around a closed path is zero ($"oint \vec{E} \cdot d\vec{l} = 0$).
• Non-conservative Fields: An electric field induced by a changing magnetic field is non-conservative ($"oint \vec{E} \cdot d\vec{l} = -\frac{d\Phi_B}{dt} \neq 0$), and its field lines form closed loops.
• No Intersection: Field lines never intersect.

2. Properties of Magnetic Field Lines

• No Sources or Sinks: Magnetic field lines always form closed loops. They do not have starting or ending points. This is a consequence of Gauss's law for magnetism, $\oint \vec{B} \cdot d\vec{A} = 0$, which implies the non-existence of magnetic monopoles.
• No Intersection: Field lines never intersect.

3. Analysis of the Options

• Option A: This pattern shows uniform, parallel, and equally spaced field lines.

  • Electric Field: This is a valid pattern. It represents the uniform electric field found between the plates of a large, parallel-plate capacitor.
  • Magnetic Field: This is also a valid pattern. It represents the uniform magnetic field inside a long, ideal solenoid.
  • Conclusion: This pattern is valid for both electric and magnetic fields.

• Option B: This pattern shows closed loops (concentric circles).

  • Electric Field: This pattern is not valid for an electrostatic field. However, it is valid for an induced electric field, such as the one generated by a changing magnetic flux through the loops.
  • Magnetic Field: This is a valid and common pattern. It represents the magnetic field lines around a long, straight, current-carrying wire.
  • Conclusion: This pattern is valid for magnetic fields and non-electrostatic electric fields.

• Option C: This pattern shows field lines radiating outwards from a single point.

  • Electric Field: This is a valid pattern. It represents the electric field of a positive point charge (an electric monopole).
  • Magnetic Field: This is not a valid pattern. It implies the existence of a magnetic monopole (a source of magnetic field), which is forbidden by Gauss's law for magnetism ($"nabla \cdot \vec{B} = 0$). Magnetic field lines cannot originate from a point.
  • Conclusion: This pattern is valid for an electric field but not for a magnetic field.

• Option D: This pattern shows field lines originating from one point and terminating at another.

  • Electric Field: This is a valid pattern, representing the field of an electric dipole (e.g., from a positive charge to a negative charge).
  • Magnetic Field: This pattern is an incorrect representation of a magnetic dipole's field. While the external field of a bar magnet looks similar, the magnetic field lines are continuous and form closed loops by passing through the magnet from the south to the north pole. The diagram incorrectly shows the lines terminating at the poles.
  • Conclusion: This pattern is valid for an electric field but is an incorrect/incomplete representation for a magnetic field.

4. Final Conclusion

Based on the analysis, Pattern A is a valid representation for both a static electric field and a static magnetic field. Pattern B is valid for a magnetic field and a time-varying electric field. Patterns C and D are invalid for magnetic fields because magnetic field lines must always form closed loops and cannot originate from or terminate at points.

The question asks which pattern is valid for both. Option A is unambiguously valid for standard cases of both fields. Therefore, Option A should be the correct answer.

However, the stored correct answer is C. This is in direct contradiction with the fundamental principle that magnetic monopoles do not exist ($"nabla \cdot \vec{B} = 0$). The pattern in C clearly depicts a field originating from a monopole source. Thus, it cannot represent a magnetic field. It appears the stored answer is incorrect.