Electric field in a certain region is given by E = (A/x²i + B/y³j). The SI unit of A and B are: (a) N m²C; N m³C (b) N m³C⁻¹; N m²C⁻¹ (c) N m³C; N m²C (d) N m²C⁻¹; N m³C⁻¹

Answer: (d). Each term must have the unit of E, i.e. N C⁻¹. A/x² = N C⁻¹ ⇒ A = N m²C⁻¹ B/y³ = N C⁻¹ ⇒ B = N m³C⁻¹ So the answer is (d).

Electric field in a certain region is given by E = (A/x²i + B/y³j)… | JEE Main 2023 (30 Jan, Shift 1)

Q19JEE Main 2023 · 30 JAN · SHIFT 1Easy

Electric Field & Field Lines

Electric field in a certain region is given by $\vec{E} = \left(\frac{A}{x^2}\hat{i} + \frac{B}{y^3}\hat{j}\right)$ . The $\text{SI}$ unit of $A$ and $B$ are:

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Answer: (d)

Each term must have the unit of $E$ , i.e. $\text{N C}^{-1}$ .
$\dfrac{A}{x^2} = \text{N C}^{-1} \Rightarrow A = \text{N m}^2\text{C}^{-1}$
$\dfrac{B}{y^3} = \text{N C}^{-1} \Rightarrow B = \text{N m}^3\text{C}^{-1}$
So the answer is (d).

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