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This is a multiple choice answer as classified in NCERT Exemplar

(c) Electric potential are always less in the direction of electric field

E= - $\frac{dv}{dr}$ and W= qdv . so potential energy also decrease in the direction of electric field

This is a multiple choice answer as classified in NCERT Exemplar

(d) We know that I=  $\frac{v}{R+r}$ = $\frac{2.5}{2+0.5}$ = 1 A

The potential difference across 2 ohm = 1 (2)= 2V

As Q=CV = 4 $\times$ 2= 8 μC

The difference between Khan Academy's prep and digital SAT prep is that,

• Khan Academy not just provides mock tests, they also have teaching videos to aid applicants with SAT prep.
• Khan Academy is the official partner of College Board for SAT exam prep after it became digitalised.
• On the other hand, College Board just has practice papers in PDF formats that can be downloaded for practice. 
• College Board does not give any prep material.
• Also, only when applicants register for SAT, can they access Bluebook App where they can take mocks in the exact same format as they will on the exam day.

This is a short answer type question as classified in NCERT Exemplar

Let us take a point p to be at a distance z from the center of ring

V=K $\int \frac{dq}{r}=k$ $\frac{dq}{\sqrt[]{z^2+a^2}}$  = $\frac{k}{\sqrt[]{z^2+a^2}}\int dq$ = $\frac{kQ}{\sqrt[]{z^2+a^2}}$

This is a short answer type question as classified in NCERT Exemplar

Let us take a point p to be at a distance z from the center of ring

V=K $\int \frac{dq}{r}=k$ $\frac{dq}{\sqrt[]{z^2+a^2}}$  = $\frac{k}{\sqrt[]{z^2+a^2}}\int dq$ = $\frac{kQ}{\sqrt[]{z^2+a^2}}$

 

U= w =qV= $\frac{kQ(-q)}{\sqrt[]{z^2+a^2}}$ = $\frac{-KQq}{\sqrt[]{z^2+a^2}}$

Charge would perform oscillations.

Well this depends on the level of SAT preparation an applicant has done. In case he has enough time, he must take as many practice tests as possible to strengthen preparation. If not, then appearing for a full mock test is absolutely necessary before the main exam day. 

This is a short answer type question as classified in NCERT Exemplar

According to the relation that E= - $\frac{dv}{dr}$ , potential always decrease in the direction of electric field . so if we go from any point to infinity that decreases the potential.

This is a short answer type question as classified in NCERT Exemplar

If there is a potential then E? 0 electric field comes into existence, which is given by as E=-dV/dr
It means there will be field lines pointing inwards or outwards from the surface. These lines cannot be again on the surface, as the surface is equipotential. It is possible only when the other end of the field lines are originated from the charges inside. Hence, the entire volume inside must be equipotential.

Yes. Getting accepted by the university of Michigan is generally considered tough because of the low acceptance rate the university has over the years. The acceptance rate of UMichigan is around 18%, which can be considered quite competitive. Generally, applicants must aim to have a good average GPA, (3.5+ on a scale of 4.0), meeting the english language requirement as prescribed by the university and submission of all the necessary documents as per the programme requirements on time.

This is a short answer type question as classified in NCERT Exemplar

As the electric field and force both are conservative so work done in conservative body as the body is closed is zero.

University of Michigan does not consider GRE scores as an mandatory admission requirement. However providing the score might strengthen and enhance the candidate's profile and increase the cahnces of acceptance. Same goes with the other standardized test scores like ACT, SAT and GMAT. GMAT scores might be considered mandatory for the MBA program. Applicants are also requested to focus on other admssion requirements like meeting the academic and english language criteria along with submission of necessary documents on an early basis.

Applicants can access official digital SAT practice tests as part of their preparation either at College Board's website or at Khan Academy website which is the official partner of College Board for preparation and practice. Once applicants register for SAT, they can set up their account on Bluebook App and take a mock test there also.