In the formula, a = 3 b c 2 , a and c have dimensions of electric capacitance and magnetic field…

In the formula, a = 3 b c 2 ,  a and c have dimensions of electric capacitance and magnetic field respectively. The dimensions of b in  S . I . system if Q denotes electric charge, are
  1. [ M - 3 L - 2 T 4 Q 4 ]
  2. [ M - 3 T 4 Q 4 ]
  3. [ M - 3 T 3 Q ]
  4. [ M - 3 L 2 T 4 Q - 4 ]

Solution

Given, a = 3 b c 2 ⇒    b = a 3 c 2 Writing dimensions for a and c , we have b = Q / V B 2 = Q [ M L 2 T - 2 Q - 1 ] - 1 M T - 1 Q - 1 2      = [ M - 3 L - 2 T 4 Q 4 ] ,

Asked in: JEE Mains - Units and Dimensions - Test 3

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