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JEE Main 202330 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
30 January
Shift
Morning Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2023 · 30 January · Morning Shift · Physics · Units and Dimensions

Electric field in a certain region is given by → E = ( A x ^ 2 ^ i...

Electric field in a certain region is given by \overset{\to}{E} = \left(\dfrac{A}{{x}^{2}}\overset{^}{i} + \dfrac{B}{{y}^{3}}\overset{^}{j}\right). The SI unit of AA and BB are :

Options

  1. ANm3C−1;Nm2C−1N{m}^{3}{C}^{- 1}; N{m}^{2}{C}^{- 1}
  2. BNm2C−1;Nm3C−1N{m}^{2}{C}^{- 1}; N{m}^{3}{C}^{- 1}
  3. CNm3C;Nm2CN{m}^{3}C; N{m}^{2}C
  4. DNm2C;Nm3CN{m}^{2}C; N{m}^{3}C

Correct answer

B. Nm2C−1;Nm3C−1N{m}^{2}{C}^{- 1}; N{m}^{3}{C}^{- 1}

Step-by-step solution

\overset{\to}{E} = \dfrac{A}{{x}^{2}}\overset{^}{i} + \dfrac{B}{{y}^{3}}\overset{^}{j}

Here, the units of Ax2andBy3\dfrac{A}{{x}^{2}} and \dfrac{B}{{y}^{3}} is equal to unit of electric field.

The unit of electric field is NC−1N{C}^{- 1}.

So, the SI unit of AA is \left[\dfrac{A}{{x}^{2}}\right] = N{C}^{- 1} ⇒ \left[A\right] = N{m}^{2}{C}^{- 1}</p><p>AndtheSIunitof</p><p>And the SI unit ofBis[By3]=NC−1⇒[B]=Nm3C−1is \left[\dfrac{B}{{y}^{3}}\right] = N{C}^{- 1} ⇒ \left[B\right] = N{m}^{3}{C}^{- 1}

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