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JEE Advanced2021PhysicsUnits and DimensionsActual

A physical quantity S → is defined as S → = E → × B → μ 0 . where E → is electric field, B → is magnetic field and μ 0 is the permeability of free space. The dimensions of S → are the same as the dimensions of which of the following quantity/quantities?

Options

  1. AEnergy Charge × Current
  2. BForce Length × Time
  3. CEnergy Volume
  4. DPower Area

Correct answer

B. Force Length × Time

Step-by-step solution

Dimension of Force Length × Time = MLT - 2 LT = MT - 3 Dimensions of Power Area = Force × Velocity Area = MLT - 2 × LT - 1 L 2 = MT - 3 , Dimension of Electric field E ,   E = MA - 1 LT - 3 Dimensions of Magnetic field B ;   B = MA - 1 T - 2 Dimension of magnetic permeability μ 0 ;   μ 0 = MA - 2 T - 2 L Therefore, dimensions of S , S = E B μ 0 = MA - 1 LT - 3 MA - 1 T - 2 MA - 2 T - 2 L = MT - 3

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