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In the formula X = 5Y Z², X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

1. [M⁻³ L⁻² T⁸ A⁴]
2. [M⁻² L⁻² T⁶ A³]
3. [M⁻¹ L⁻² T⁴ A²]
4. [M⁻² L⁰ T⁻⁴ A⁻²]

Correct answer: [M⁻³ L⁻² T⁸ A⁴]

Solution

The correct option is right because, in the equation, the dimensions of X (capacitance) and Z (magnetic field) must be balanced with Y. By analyzing the dimensions of capacitance and magnetic field, we can derive the necessary dimensions for Y, which results in [M⁻³ L⁻² T⁸ A⁴].

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