Write the expression for Lorentz magnetic force on a particle of charge ‘q’ moving with velocity v in a magnetic field B . Show that no work is done by this force on the charged particle.
ORA steady current (I1) flows through a long straight wire. Another wire carrying steady current (I2) in the same direction is kept close and parallel to the first wire. Show with the help of a diagram how the magnetic field due to the current I1 exerts a magnetic force on the second wire. Write the expression for this force.
Lorentz magnetic force is given by,
Therefore, work done is,
So, Work done, W = 0
Consider two long straight conductors PQ and RS placed parallel to each other carrying currents I1 and I2 respectively. Conductors experience an attractive force when the conductors move in the same direction while, repulsive force is experienced by the conductors when currents move in opposite direction.
PQ and RS which are placed at a distance r, carry currents I1 and I2 in the same direction.
Suppose, a current element ‘ab’ of length of wire RS.
The magnetic field produced by current-carrying conductor PQ at the location of other wire RS,
So, total force on the conductor of length L is given by,
Force acting per unit length of conductor is given by,
Define electric dipole moment. Write its S.I. unit.
Electric dipole moment is defined as the product of charge and the distance between the charges, and is directed from negative to positive charge.
The SI unit of electric dipole moment is coulomb metre (Cm).
What are eddy currents? Write any two applications of eddy currents.
Eddy currents are the currents induced in a metallic plate when it is kept in a time varying magnetic field. Magnetic flux linked with the plate changes and so the induced current is set up. Eddy currents are sometimes so strong, that metallic plate becomes red hot.
A thin straight infinitely long conducting wire having charge density is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.
Given, charge density =
Radius and length of the cylindrical surface are r and l respectively.
Charge enclosed by the cylindrical surface = l
Now, using Gauss theorem,
A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. What is the potential at the centre of the sphere?
Potential at centre of sphere is equal to 10 V.
Two bar magnets are quickly moved towards a metallic loop connected across a capacitor ‘C’ as shown in the figure. Predict the polarity of the capacitor.
Left face of the coil will act as North Pole and right face as South Pole so as to oppose the current induced in the coil. As seen from left, the direction of the current in the coil will be anti-clockwise.
That is, plate of the capacitor A will be positive and plate B will be negative.
Upper plate is positive and lower plate is negative.
In the given circuit, assuming point A to be at zero potential, use Kirchhoff’s rules to determine the potential at point B.
Current in 2 resistor is 1 A.
Now, applying Kirchhoff’s law ACDB,
VA + 1 + 2 x 1 - 2 = VB
As, VA = 0
VB = 1 + 2 - 2 = 1 V
Plot a graph showing the variation of coulomb force (F) versus , where r is the distance between the two charges of each pair of charges: (1 C, 2 C) and (2 C – 3 C). Interpret the graphs obtained.
Force between charged particles is given by,
The graph between F and is a straight line of slope passing through the origin.
Magnitude of slope is more for attraction, therefore attractive force is greater than the repulsive force.
How are radio waves produced?
Radio waves are produced by the accelerated motion of charges in conducting wires.