The law which states that the variations of electric field causes magnetic field is

Options

A. Faraday's law
B. Biot-Savart law
C. modified Ampere's law
D. Lenz's law

Explanation

To solve the question, we need to identify the law that states the relationship between the variations of the electric field and the magnetic field.

### Step-by-Step Solution:

1. **Understanding the Context**: We are looking for a law in electromagnetism that describes how a changing electric field can induce a magnetic field.

2. **Identify the Relevant Law**: The law that describes this relationship is known as the Modified Ampere's Law, which is often referred to as Maxwell's Ampere Law.

3. **Formulation of the Law**: According to Maxwell's Ampere Law, the integral of the magnetic field (B) around a closed loop (dl) is equal to the permeability of free space (μ₀) multiplied by the total current (I) passing through the loop. This can be expressed mathematically as:
\[ \oint B \cdot dl = \mu_0 (I_C + I_D) \]
where:
- \(I_C\) is the conduction current (due to the flow of charges),
- \(I_D\) is the displacement current (due to the changing electric field).

4. **Displacement Current**: The displacement current \(I_D\) is defined as:
\[ I_D = \epsilon_0 \frac{d\Phi_E}{dt} \]
where \(\Phi_E\) is the electric flux. This term accounts for the changing electric field in a region.

5. **Conclusion**: Therefore, the law that states that variations in the electric field cause a magnetic field is the Modified Ampere's Law, also known as Maxwell's Ampere Law.

### Final Answer:
The law which states that the variations of electric field cause magnetic field is the Modified Ampere's Law (Maxwell's Ampere Law).

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