Vectors – JEE First

Imagine a mass $m$ moving on the surface of a rotating sphere. For instance, the mass could be parcel of air moving away from a high pressure region in the Earth’s atmosphere. It experiences a Coriolis force which, in the example shown in the figure below, pushes it from its original trajectory (orange) to move eastward (blue). Why does this happen, and how do we understand it intuitively?

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Formally, the Coriolis force on $m$ is given by

(1) $\begin{equation*} {\bf F}_{\rm Coriolis} = - 2 m {\bf \Omega} \times {\bf v}_{\rm rot} , \end{equation*}$

where ${\bf \Omega}$ is the angular velocity of the rotating frame (Earth), and ${\bf v}_{\rm rot}$ is the velocity of $m$ as seen by an observer on the Earth’s …

JEE Advanced 2019 Paper 2, Question 4

An electric dipole with dipole moment $\frac{p_{0}}{\sqrt{2}}(\hat{i}+\hat{j})$ is held fixed at the origin $O$ in the presence of an uniform electric field of magnitude $E_{0}$ . If the potential is constant on a circle of radius $R$ centered at the origin as shown in figure, then the correct statement(s) is/are:

( $\varepsilon_{0}$ is permittivity of free space. $R \gg$ dipole size)

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$R=\left(\frac{p_{0}}{4 \pi \epsilon_{0} E_{0}}\right)^{1 / 3}$
Total electric field at point $A$ is ${\bf E}^A=\sqrt{2} E_{0}(\hat{i}+\hat{j})$
Total electric field at point $B$ is ${\bf E}^B=0$
The magnitude of total electric field on any two points of the circle will be same.

Solution

The potential due to the dipole kept at the origin …

Tag: Vectors

Coriolis effect and angular momentum

Dipole in a uniform electric field