Question

A non-conducting ring of the radius \[R\] has a charge \[Q\] distributed unevenly over it. If it rotates with an angular velocity \[\omega \], the equivalent current will be:
A.Zero
B.\[Q\omega \]
C.\[\dfrac{{Q\omega }}{{2\pi }}\]
D.\[Q\dfrac{\omega }{{2\pi R}}\]

Answer 1

Hint: We need to find the equivalent current that is passing through the non-conducting ring of radius \[R\] in which the charge \[Q\] is unevenly distributed. We know that current is equal to charge crossing per second. Every time the ring rotates the charge \[Q\] will cross any fixed point near the ring. Using this concept we will solve the above problem.

Complete answer:
Given that the radius of the non-conducting ring is \[R\]. The charge that is unevenly distributed over the ring is \[Q\]. It rotates with an angular velocity that is given by \[\omega \].
The time period with which the charge rotates is given by, \[T = \dfrac{{2\pi }}{\omega }\]
Now we already said that current is equal to the number of charges crossing any fixed point per second. The formula for the current is given as,
\[ \Rightarrow I = \dfrac{Q}{T}\] ……. (1)
Here,
 \[Q\] is the charge
 \[T\] is the time period.
Therefore substituting all the known values in the above equation we get,
\[ \Rightarrow I = \dfrac{{Q\omega }}{{2\pi }}\]
The above equation gives us the equivalent current that is passing in the non-conducting ring is found to be \[\dfrac{{Q\omega }}{{2\pi }}\].

Therefore, the correct option is C.

Note:
The rate of flow of electrons in a conductor is defined as the electric current. We measure electric current in the units of Ampere. Conductors are defined as the materials that allow an electric current to pass through them. The best conductor of electricity is found to be Silver. Angular velocity is defined as the rate of speed at which an object rotates. The angular velocity is usually denoted by the letter \[\omega \].