Q. 25.0( 1 Vote )

# 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. x, y have the same dimension.B. y, z have the same dimensionsC. z, x have the same dimensionsD. None of the three pairs have the same dimensions.

(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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Magnetic field due to current carrying straight wire37 mins
Magnetic field due to current carrying circular loop36 mins
Interactive Quiz on Magnetic field due to straight wire & circular loop41 mins
Gain Confidence on Magnetic Effects of Current with Questions41 mins
Equation of electric and magnetic field52 mins
Magnetic force on moving charge particle in magnetic field | Quiz32 mins
Magnetic force on moving charge particle in magnetic field44 mins
Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)47 mins
Few Applications of Gauss's law54 mins
Electric field inside cavity37 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses