JEE Main 2023 · 30 January · morning · Single correct · +4 / −1
Electric field in a certain region is given by E⃗=(A/x² î+B/y³ ĵ) . The SI unit of A and B are :
- (a) Nm² C ; Nm³ C
- (b) Nm³ C⁻¹ ; Nm² C⁻¹
- (c) Nm³ C ; Nm² C
- (d) Nm² C⁻¹ ; Nm³ C⁻¹
Answer and solution
Answer (d) Nm² C⁻¹ ; Nm³ C⁻¹
Solution
Physics sir · 4 steps
Each term must have the units of E, so A carries one extra m² and B one extra m³.
- Unit of E. Electric field is force per unit charge, so its SI unit is N C⁻¹. Every term added inside E⃗ must have this same unit.
- Find A. A/x² has the unit N C⁻¹ and x² is in m². So A must be in N m² C⁻¹.
[A] = [E] [x²] = N m² C⁻¹, [B] = [E] [y³] = N m³ C⁻¹
- Find B. B/y³ also has the unit N C⁻¹ and y³ is in m³. So B must be in N m³ C⁻¹.
- So. A is in N m² C⁻¹ and B is in N m³ C⁻¹, which is option (d).
The idea to keep. When a constant sits over a power of length, multiply the unit of the quantity by that same power of metres. The unit of E always keeps C⁻¹, so the constants do too.
Answer from the NTA final answer key. Solution by PrepWiser.