Consider three quantities x = E/B, y = and
. Here, ℓ is the length of a wire, C is a capacitance and R is a resistance. All other symbols have standard meanings.
(A)Dimension for electric field E is: F/q = [MLT-3A-1]
Force due to magnetic field is given as: F=qvB.
Where q is the charge, v is the velocity of charge and B is the magnetic field.
Hence
The dimensions of charge, q is [AT]
The dimension of the velocity, V is [LT-1]
Putting the value in the above formula, we get
Dimensions of B =
∴ Dimensions of B = [MT-2A-1]
Thus,
(B)
We know that Where
μ0 is permeability of free space,
ϵ0 is the permittivity of free space and
c is the speed of light.
Thus, y = c, c is the speed and unit of speed is m/s
Dimensions of y = [LT-1]
(C)
Reactance,
Where
C is the capacitance
R is the resistance
l is the length of the wire.
In a CR circuit the product CR is the time constant and unit is seconds.
Thus, Dimensions of z = l/CR = m/s= [LT-1]
Hence x, y and z have same dimensions.
Thus, options (A),(B) and (C) are the correct options.