Q: A few electric field lines for a system of two charges \$Q_{1}\$ and \$Q_{2}\$ fixed at two different points on the \$x\$-axis are shown in the figure. These lines suggest that

Number of Electric field lines emerging from \$Q_1\$ are more than the number of lines terminating at \$Q_2\$.So , \$Q_1\$ is a positive charge of higher magnitude and \$Q_2\$ is a negative charge of smaller magnitude .Hence , the point at which the electric field is zero is on the right of the negative charge \$Q_2\$

Q: Consider an electric field \$\overline{E}=E_{0}\hat{x}\$, where \$E_{0}\$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is:

\$Flux\ through\ area = Electric\ field \times Area\ projected\$\$\phi =EA cos45^o\$ \$= E_0(\sqrt{2}a^2) \times \dfrac{1}{\sqrt2}\$ \$= E_0a^2\$

Q: A point charge \$+Q\$ is placed just outside an imaginary hemispherical surface of radius \$R\$ as shown in the figure. Which of the following statements is/are correct?

\$\phi = \dfrac{q}{2 \epsilon_0}(1-cos \phi)\$\$Here, \phi=\dfrac{\pi}{4}\$So, \$\phi=\dfrac{q}{2\epsilon_0}(1-\dfrac{\pi}{4})\$\$\phi=\dfrac{-q}{2\epsilon_0}(1-\dfrac{1}{\sqrt{2}})\$Also the circumference of the flat surface is an equipotential.

Q: A cubical region of side a has its centre at the origin. It encloses three fixed point charges, -qat (0, -a/4, 0), +3q at (0, 0, 0) and -q at (0, +a/4 ,0). Choose the correct option(s):

\$ \text{Net flux through cube} \$= \$\displaystyle \frac{-q + 3q -q}{\epsilon_{o}} = \frac{q}{\epsilon_{o}}\$\$\text{Due to the same area flux passing through}\$ \$\displaystyle x= \frac{-a}{2}, y= \frac{a}{2}\$ \$and\$ \$\displaystyle z=\frac{a}{2}\$ \$\text{is same}\$

Q: Let E\$_1\$(r), E\$_2\$(r) and E\$_3\$(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density \$\lambda\$, and an infinite plane with uniform surface charge density \$\sigma\$. If E\$_1(r_0) = E_2 (r_0) = E_3 (r_0)\$ at a given distance r\$_0\$, then :

\$\displaystyle \frac{Q}{4 \pi \varepsilon_0r_0^2}=\frac{\lambda}{2 \pi \varepsilon_0 r_0} = \frac{\sigma}{2 \varepsilon_0}\$\$\displaystyle E_1 \left ( \frac{r_0}{2} \right ) = \frac{Q}{\pi \varepsilon_0r_0^2}, E_2 \left ( \frac{r_0}{2} \right ), E_3 \left ( \frac{r_0}{2} \right ) = \frac{\sigma}{2 \varepsilon_0}\$\$\displaystyle \therefore E_1 \left ( \frac{r_0}{2} \right ) = 2E_2 \left ( \frac{r_0}{2}\right)\$

Question 1

A few electric field lines for a system of two charges $Q_{1}$ and $Q_{2}$ fixed at two different points on the $x$-axis are shown in the figure. These lines suggest that

Accepted Answer

Number of Electric field lines emerging from $Q_1$ are more than the number of lines terminating at $Q_2$.So , $Q_1$ is a positive charge of higher magnitude and $Q_2$ is a negative charge of smaller magnitude .Hence , the point at which the electric field is zero is on the right of the negative charge  $Q_2$

Question 2

Consider an electric field $\overline{E}=E_{0}\hat{x}$, where $E_{0}$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is:

Accepted Answer

$Flux\  through\  area = Electric\  field  \times Area\  projected$$\phi =EA cos45^o$       $= E_0(\sqrt{2}a^2) \times \dfrac{1}{\sqrt2}$         $= E_0a^2$

Question 3

A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?

Accepted Answer

$\phi = \dfrac{q}{2 \epsilon_0}(1-cos \phi)$$Here, \phi=\dfrac{\pi}{4}$So, $\phi=\dfrac{q}{2\epsilon_0}(1-\dfrac{\pi}{4})$$\phi=\dfrac{-q}{2\epsilon_0}(1-\dfrac{1}{\sqrt{2}})$Also the circumference of the flat surface is an equipotential.

Question 4

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, -qat (0, -a/4, 0), +3q at (0, 0, 0) and -q at (0, +a/4 ,0). Choose the correct option(s):

Accepted Answer

$ \text{Net  flux  through  cube} $= $\displaystyle \frac{-q + 3q -q}{\epsilon_{o}} = \frac{q}{\epsilon_{o}}$$\text{Due  to  the  same  area  flux  passing  through}$ $\displaystyle x= \frac{-a}{2}, y= \frac{a}{2}$ $and$ $\displaystyle z=\frac{a}{2}$ $\text{is  same}$

Question 5

Let E$_1$(r), E$_2$(r) and E$_3$(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density $\lambda$, and an infinite plane with uniform surface charge density $\sigma$. If E$_1(r_0) = E_2 (r_0) = E_3 (r_0)$ at a given distance r$_0$, then :

Accepted Answer

$\displaystyle \frac{Q}{4 \pi \varepsilon_0r_0^2}=\frac{\lambda}{2 \pi \varepsilon_0 r_0} = \frac{\sigma}{2 \varepsilon_0}$$\displaystyle E_1 \left ( \frac{r_0}{2} \right ) = \frac{Q}{\pi \varepsilon_0r_0^2}, E_2 \left ( \frac{r_0}{2} \right ), E_3 \left ( \frac{r_0}{2} \right ) = \frac{\sigma}{2 \varepsilon_0}$$\displaystyle \therefore E_1 \left ( \frac{r_0}{2} \right ) = 2E_2 \left ( \frac{r_0}{2}\right)$

Electric Charges And Fields

Physics
4019 Views

A few electric field lines for a system of two charges $Q_{1}$ and $Q_{2}$ fixed at two different points on the $x$ -axis are shown in the figure. These lines suggest that

Consider an electric field $\overline{E} = E_{0} \overset{x}{^}$ , where $E_{0}$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is:

A point charge $+ Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, -q
at (0, -a/4, 0), +3q at (0, 0, 0) and -q at (0, +a/4 ,0). Choose the correct option(s):

Electric Charges And Fields

Physics 4019 Views

A few electric field lines for a system of two charges Q1​ and Q2​ fixed at two different points on the x-axis are shown in the figure. These lines suggest that

Consider an electric field E=E0​x^, where E0​ is a constant. The flux through the shaded area (as shown in the figure) due to this field is:

A point charge +Q is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, -q at (0, -a/4, 0), +3q at (0, 0, 0) and -q at (0, +a/4 ,0). Choose the correct option(s):

Physics
4019 Views

A few electric field lines for a system of two charges $Q_{1}$ and $Q_{2}$ fixed at two different points on the $x$ -axis are shown in the figure. These lines suggest that

Consider an electric field $\overline{E} = E_{0} \overset{x}{^}$ , where $E_{0}$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is:

A point charge $+ Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, -q
at (0, -a/4, 0), +3q at (0, 0, 0) and -q at (0, +a/4 ,0). Choose the correct option(s):