A dipole of moment \(\overrightarrow{p}\) is placed in uniform electric field \(\overrightarrow{E}\) then torque acting on it is given by : -
Four point charges \(q_A\)\( = 2 µC\), \(q_B\) \(= −5 µC\), \(q_C\) = 2 µC, and \(q_D\) \(= −5 µC\) are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 µC placed at the centre of the square?
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude \(17.0 × 10^{−22} Cm^{-2}\). What is E:
(a) in the outer region of the first plate,
(b) in the outer region of the second plate, and (c) between the plates?
Consider a water tank shown in the figure. It has one wall at \(x = L\) and can be taken to be very wide in the z direction. When filled with a liquid of surface tension \(S\) and density \( \rho \), the liquid surface makes angle \( \theta_0 \) (\( \theta_0 < < 1 \)) with the x-axis at \(x = L\). If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is: (take \(g\) as the acceleration due to gravity)
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :