# 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-

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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-
1. g cm
2. N m2
3. m s-1
4. kg m-2

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Correct Answer - Option 4 : kg m-2

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:
 Fundamental quantity Dimension Time T Mass M Electric current A Thermodynamic temperature K Amount of substance mol Luminous intensity cd Length L

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