Question

The dimensional formula for the magnetic fields is
$\begin{align}
  & \text{A}\text{. }\left[ M{{T}^{-2}}{{A}^{-1}} \right] \\
 & \text{B}\text{. }\left[ M{{L}^{2}}{{T}^{-1}}{{A}^{-2}} \right] \\
 & \text{C}\text{. }\left[ M{{T}^{-2}}{{A}^{-2}} \right] \\
 & \text{D}\text{. }\left[ M{{T}^{-1}}{{A}^{-2}} \right] \\
\end{align}$

Answer 1

Hint: We know that the force a magnetic field exerts on a charge q moving with velocity v is called the magnetic force. To find the dimension, use the expression of magnetic force which gives a relation between charge, velocity and magnetic field. Calculate dimension for each of the terms like force, charge and velocity and calculate dimension of magnetic field.

Formula used:
Formula used:
Expression of Magnetic force is given by.
 \[F=qvB\]
Where,
F= force
q= charge
v= velocity
B=magnetic field

Complete answer:
Generally, all the physical quantities of interest can be derived from the base quantities, when a quantity is expressed in terms of the base quantities then it can be written as a product of different- different powers of the base quantities. The exponent of a base quantity that enters into the expression, is known as the dimension of the quantity in that base.
The force a magnetic field exerts on a charge q moving with velocity v is called the magnetic force and it is given by,
\[F=qvB-----(1)\]
Rearrange, we get
$B=\dfrac{F}{v\times q}$
Dimension of force F is $\left[ ML{{T}^{-2}} \right]$
Dimension of force v is $\left[ L{{T}^{-1}} \right]$
Dimension of force q is $\left[ AT \right]$
Put all the values in above equation, we get
\[B=\dfrac{F}{v\times q}=\dfrac{\left[ ML{{T}^{-2}} \right]}{\left[ L{{T}^{-1}} \right]\left[ AT \right]}=\left[ M{{T}^{2}}{{A}^{-1}} \right]\]

So, the correct answer is “Option A”.

Additional Information:
In 1820 Hans Christian Oersted, a Danish physicist, discovered that there is a relationship between current electricity and magnetism. He found that a wire carrying current causes a deflection of a magnetic needle placed near the wire. He concluded that when electric current passes through a conductor, a magnetic field is produced around it.

The direction of the magnetic field produced depends upon the direction the current passes through the conductor. This direction of the magnetic field can be obtained by using right hand rule. The deflection of the needle increases with increases in the magnitude of the current. It shows that strength of magnetic field depends upon current flowing through a wire. This phenomena is known as magnetic effect of electric current.

Note:
Equation (1) is applicable for moving charges and it is also known as magnetic Lorentz force. Students usually mug the dimension but rather than mugging you can use a formula of at least definition. Direction of the magnetic field can be obtained by using right hand rule.