In a particle accelerator, a current of $500 \,\mu A$ is carried by a proton beam in which each proton has a speed of $3 \times 10^7 \,m / s$. The cross-sectional area of the beam is $1.50 \,mm ^2$. The charge density in this beam (in $C / m ^3$ ) is close to
$10^{-8}$
$10^{-7}$
$10^{-6}$
$10^{-5}$
The electric field $\vec E$ between two points is constant in both magnitude and direction. Consider a path of length d at an angle $\theta = 60^o$ with respect to field lines shown in figure. The potential difference between points $1$ and $2$ is
Two capacitor one of capacitance $C$ and other capacitance $C/2$ are connected with a battery of $V$ $volt$ then heat produced in connecting wire
Two condensers $C_1$ and $C_2$ in a circuit are joined as shown in figure. The potential of point $A$ is $V_1$ and that of $B$ is $V_2$. The potential of point $D$ will be
A parallel plate capacitor with air between the plates has a capacitance of $9\ pF$ . The separation between its plates is $ 'd'$ .The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac {d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now ......... $pF$
A series combination of $n_1$ capacitors, each of value $C_1$, is charged by a source of potential difference $4\,V$. When another parallel combination $n_2$ capacitors, each of value $C_2$, is charged by a source of potential difference $V$, it has the same (total) energy store in it, as the first combination has. The value of $C_2$, in terms of $C_1$, is then