Figure shows a solid hemisphere with a charge of 5nC distributed uniformly throughout its volume. The hemisphere lies on a plane and point P is located on the plane, along a radial line from the centre of curvature at distance 15cm. The electric potential at point P (in volts) due to the hemisphere, is___.
By argument of symmetry, it will be half of the potential produced by the full sphere
∵ – Charge on hemisphere = Q, so charge on sphere = 2Q
The correct answer is: 300
A simple pendulum with a bob of mass m = 1kg, charge q = 5μC and string length l = 1m is given a horizontal velocity u in a uniform electric field E = 2 × 106 V/m at its bottom most point A, as shown in figure. It is given that the speed u is such that the particle leaves the circle at point C. Find the speed u.
(Take g = 10m/s2)
From work-energy theorem,
Substituting the values, we get
Further, at C tension in the string is zero
or v2 = 3.66 ......(ii)
From Eqs. (i) and (ii), we get
u = 6m/s
The correct answer is: 6
A position charge +Q is fixed at a point A. Another positively charged. particle of mass m and charge +q is projected from a point B with velocity u as shown in the figure. The point B is large distance from A and at distance d from the line AC. The initial velocity is parallel to the line AC. The point C is at very large distance from A. Find the minimum distance (in meter) of +q from +Q during the motion.
The path of the particle will be as shown in the figure. At the point of minimum distance (D) the velocity of the particle will be to its position vector w.r.t +Q.
∵ Torque on q about Q is zero hence angular momentum about Q will be conserved
⇒ mvrmin = mud ........(2)
by (2) in (1)
∵ distance cannot be negative
The correct answer is: 1
The electric potential varies in space according to the relation V = 3x + 4y. A particle of mass 10kg starts from rest from point (2,3.2)m under the influence of this field. Find the velocity of the particle in units of 10–3m/s, when it crosses the x-axis. The charge on the particle is 1μC. Assume V(x,y) are in SI units.
When particle crosses x-axis, y = 0
Initial y-coordinate was 3.2 m and
At this instant x-coordinate will be,
The correct answer is: 2
Consider a cube of side a = 0.1m placed such that its six faces are given by equations x = 0, x = + a, y = 0, y = +a, z = 0 and z = +a, placed in electric field given by Find the electric flux crossing out of the cube in the unit of
Flux through ABCD.
Flux through BCGF
Flux through CDHG
The correct answer is: 11
A solid sphere of radius R has a cavity of radius R/2 The solid part has a uniform charge density ρ and cavity has no charge. The electric potential at point A is then value of x is
Assume a solid sphere without cavity.
Potential at A due to this solid sphere
Electric field at C due to this solid sphere
Now consider the cavity filled with negative charge
Now net values for the solid sphere with the cavity can be given by superposition of the above two cases
The correct answer is: 12
A graph of the x component of the electric field as a function of x in a region of space is shown. The y and z components of the electric field are zero in this region. If the electric potential is 10V at the origin, then potential (in volts) at x = 2.0m is
The correct answer is: 30
A dipole of dipole moment is placed at point A(2, -3, 1). The electric potential due to this dipole at the point B(4, -1, 0) is equal to n × 109 volts. Find the value of n.
The correct answer is: -2
A 4.00 kg block carrying a charge Q = 50.0μC is connected to a spring for which k = 100N/m. The block lies on a friction less horizontal track, and the system is immersed in a uniform electric field of magnitude E = 5.00 × 105 V/m, directed as shown in figure. If the block is released from rest when the spring is unscratched (at x = 0). By what maximum amount does the spring expand. (Answer in meters)
By comparing this problem with spring-block system problem suspended vertically.
The correct answer is: 0.5
Three identical, conducting plane parallel plates, each of area A are held with equal separation d between successive surfaces. Charges Q, 2Q, and 3Q are placed on them. Neglecting edge effects. The sum of charges on the six surfaces is given by nQ. Find the value of n.
The correct answer is: 3