A physical quantity is given by the equation x = CB² where C is capacitance and B is the magnetic field strength. Then the SI base units of x is-

The correct answer is option 4) i.e. kg m-2

CONCEPT:

• The SI base units are the standard units of measurement.
• ​The seven base units used in the SI system are meter (m), kilogram (kg), second (s), kelvin (K), ampere (A), mole (mol), and candela (cd).
• The seven base units along with their dimensions are as follows:

EXPLANATION:

• The capacitance C is related to the charge Q and voltage V across them as: \(C =\frac{Q}{V}\)
  • Dimensions of charge, Q = current × time = [A] × [T] = [A1T1]
  • Dimensions of voltage, V = work done per unit charge = (force × displacement)(charge)^-1 = [M¹L¹T^-2][L¹] × [A¹T¹]^-1 = [M1L2A^-1T-3]
  • Dimensions of capacitance, \( C =\frac{[A^1T^1]}{[M^1L^2A^{-1}T^{-3}]} = [M^{-1}A^2L^{-2}T^4]\)
• A charged particle (q) moving with a speed (v) relative to a magnetic field experiences a magnetic force due to the magnetic field (B). The magnitude of this force (F) is given by

F = qvB

• Magnetic field intensity, \(B =\frac{F}{qv}\)
• Dimensions of force, F = [M¹L¹T^-2]
• Dimensions of charge, q = [A1T1]
• Dimensions of velocity, v = [L¹T^-1]
• Dimensions of \(B =\frac{[M^1L^1T^{-2}]}{[A^1T^{1}][L^1T^{-1}]} = [M^1T^{-2}A^{-1}]\)

⇒ Dimension of x = CB² = [M^-1A²L^-2T⁴] [M¹T^-2A^-1]² = [M¹L^-2]

⇒ SI base unit for [M] and [L] is kg and m respectively.

⇒ [M1L-2] = kg m-2