Verified Solution • 2025–26 Session moderate

QJEEM19Phec89: JEE Main 2019 Physics - Class 11 JEEM19Phec89 Solution: In the formula X = 5YZ 2 , X and Z have dimensions of…

In the formula X = 5YZ2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

Multiple Choice Options

  • A [M–3L–2T8A4]
  • B [M–2L–2T6A3]
  • C [M–1L–2T4A2]
  • D [M–2L0 T–4A–2]

Step-by-Step Verified Solution

Capacitance (C) = Q22E{{{Q^2}} \over {2E}} = [A2T2][ML2T−2]{{\left[ {{A^2}{T^2}} \right]} \over {\left[ {M{L^2}{T^{ - 2}}} \right]}} = [M−1L−2T4A2]\left[ {{M^{ - 1}}{L^{ - 2}}{T^4}{A^2}} \right] X

Magnetic field (B) = FIL{F \over {IL}} = [MLT−2][A][L]{{\left[ {ML{T^{ - 2}}} \right]} \over {\left[ A \right]\left[ L \right]}} = [MT−2A−1]{\left[ {M{T^{ - 2}}{A^{ - 1}}} \right]} = Z

Given,

X = 5YZ2

∴\therefore Y = X5Z2{X \over {5{Z^2}}}

[Y] = [M−1L−2T4A2][MT−2A−1]2{{\left[ {{M^{ - 1}}{L^{ - 2}}{T^4}{A^2}} \right]} \over {{{\left[ {M{T^{ - 2}}{A^{ - 1}}} \right]}^2}}}

∴\therefore [Y] = [M–3L–2T8A4]

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