Electric potential in a region is varying according to the relation $V=\frac{3 x^2}{2}-\frac{y^2}{4}$, where $x$ and $y$ are in metre and $V$ is in volt. Electric field intensity (in $N/C$) at a point $(1 \,m , 2 \,m$ ) is ......
A$3 \hat{i}-\hat{j}$
B$-3 \hat{i}+\hat{j}$
C$6 \hat{i}-2 \hat{j}$
D$-6 \hat{i}+2 \hat{j}$
Medium
Download our app for free and get started
B$-3 \hat{i}+\hat{j}$
b (b)
$V=\frac{3 x^2}{2}-\frac{y^2}{4}$
$E_x=\frac{-d V}{d x}=-3 x=-3$
$E_y=\frac{-d V}{d y}=+\frac{y}{2}=1$
$\vec{E}=-3 \hat{i}+\hat{j}$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Two similar conducting balls having charges $+q$ and $-q$ are placed at a separation $d$ from each other in air. The radius of each ball is $r$ and the separation between their centres is $d(d > > r)$. Calculate the capacitance of the two ball system
Charge is uniformly distributed on the surface of a hollow hemisphere. Let $O$ and $A$ be two points on the base of the hemisphere and $V_0$ and $V_A$ be the electric potentials at $O$ and $A$ respectively. Then,
A parallel plate capacitor has plates of area $A$ separated by distance $d$ between them. It is filled with a dielectric which has a dielectric constant that varies as $\mathrm{k}(\mathrm{x})=\mathrm{K}(1+\alpha \mathrm{x})$ where $\mathrm{x}$ is the distance measured from one of the plates. If $(\alpha \text {d)}<<1,$ the total capacitance of the system is best given by the expression
A charge is spread non-uniformly on the surface of a hollow sphere of radius $R$, such that the charge density is given by $\sigma=\sigma_0(1-\sin \theta)$, where $\theta$ is the usual polar angle. The potential at the centre of the sphere is
At the centre of a half ring of radius $R=10 \mathrm{~cm}$ and linear charge density $4 \mathrm{n} \mathrm{C} \mathrm{m}^{-1}$, the potential is $x \pi V$. The value of $x$ is . . . . .
A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is connected to another battery and is charged to potential difference $2V$. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is