Electric Field Due to a Dipole

Q. A thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the center of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the center of the shell is

1. $\frac{2Q}{4\pi {\epsilon }_{0}R}+\frac{q}{4\pi {\epsilon }_{0}R}$
2. $\frac{2Q}{4\pi {\epsilon }_{0}R}$
3. $\frac{2Q}{4\pi {\epsilon }_{0}R}-\frac{q}{4\pi {\epsilon }_{0}R}$
4. $\frac{2Q}{4\pi {\epsilon }_{0}R}+\frac{2q}{4\pi {\epsilon }_{0}R}$

Q.

An electric dipole is placed along the x - axis at the origin O . A point P is at a distance of 20cm from this origin such that OP makes an angle $\frac{\pi }{3}$ with the x-axis. If the electric field at P makes an angle θ with the x-axis, the value of $\theta$ would be

1. $\frac{\pi }{3}$
2. $\frac{\pi }{3}+ta{n}^{-1}\left(\frac{\sqrt{3}}{2}\right)$
3. $\frac{2\pi }{3}$
4. $ta{n}^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Q. what are vector laws ? why is electric current a scalar quantity though it has both magnitude and direction?

Q. Two point charges $+q$ and $-2q$ are placed at a distance $6\text{m}$ part on a horizontal plane. Find the locus of a point on this plane where the electric potential has zero value.

1. Circle with radius $4\text{m}$ and centre $(0,0)$.
2. Circle with radius $4\text{m}$ and centre $(-2,0)$.
3. Circle with radius $2\text{m}$ and centre $(-2,0)$.
4. Circle with radius $4\text{m}$ and centre $(0,-2)$.

Q. A uniform magnetic field $\overrightarrow{B}=(20\hat{i}-30\hat{j}+50\hat{k})\text{T}$ exists in the space. A charge particle with specific charge $\frac{{10}^3}{19}\text{C/kg}$ enters this region at time $t=0$ with a velocity $\overrightarrow{v}=(20\hat{i}+50\hat{j}+30\hat{k})\text{m/s}$. The pitch of the helical path for the motion of the charged particle will be:

1. $\frac{\pi }{125}\text{m}$
2. $\frac{\pi }{100}\text{m}$
3. $\frac{\pi }{250}\text{m}$
4. $\frac{\pi }{215}\text{m}$

Q. A hollow sphere contains a dipole with dipole moment 10 Cm and each charge having a magnitude of 100 C. Flux throught the sphere is .

1. 100/${ϵ}_0$
2. 200/${ϵ}_0$
3. Zero
4. Data Insufficient

Q. Consider two concentric spherical surfaces ${\text{S}}_1$ with radius $a$ and ${\text{S}}_2$ with radius $2a$, both centred on the origin. There is a charge $+q$ at the origin, and no other charges. Compare the flux ${\varphi }_1$ through ${\text{S}}_1$ with flux ${\varphi }_2$ through ${\text{S}}_2$

1. ${\varphi }_1={\varphi }_2$
2. ${\varphi }_1=\frac{{\varphi }_2}{2}$
3. ${\varphi }_1=2{\varphi }_2$
4. ${\varphi }_1=4{\varphi }_2$