Electric Circuits Answers

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Two spheres with equal but opposite charges experience a force of 7.5 106N
when they are placed 4 cm apart in a medium of relative permittivity 6.
Determine the charge on each sphere

The IR drop across resistor means there is a change in potential or voltage across the resistor. Is there any change in current as it passes through a resistor. Explain

A uniform plane wave of 100 kHz travelling in free space strikes a large block of a material having ε = 4ε0 , µ = 9µ0 and σ = 0 normal to the surface. If the incident magnetic field vector is given by
B = 10^-6 cos(ωt −βy) z^ tesla
write the complete expressions for the incident, reflected, and transmitted field
vectors.

Using Maxwell’s equations in free space, derive the wave equation for the electric field vector. Obtain the conditions under which the following time varying electric and magnetic fields satisfy Maxwell’s equations in vacuum with no source charges or currents:
E = k^E0 sin( y − vt)
B = i^B0 sin( y − vt)
where E0 and B0 are constant.

At the centre of an air core solenoid, the value of the magnetic field B is 0.40 mT. If the current flowing in the solenoid is 0.4 A, calculate the number of turns per cm.

A long, straight wire of radius 5.0 mm carries a current of 20A. i) Calculate the
magnetic field at the surface of the wire, and ii) calculate the perpendicular distance,
from the axis of the wire, at which the magnitude of magnetic field will be half of
its value at the wire surface.

Two long, straight, parallel wires A and B, separated by a distance of 30 cm, carry
currents IA = 10A and IB = 30A. The currents in both the wires flow in the same
direction. Calculate the net magnetic field at the midpoint of the line joining the two
wires and perpendicular to them.

An electron and a proton, moving with equal velocity, enter a region of uniform, perpendicular magnetic field. Calculate the ratio of the radii of their circular paths in the field.

The mass density of copper is 8.95×10^3 kg m^−3 . If one charge carrier is contributed
by each copper atom, calculate the number density of charge carriers in copper. If
5A current is flowing in a copper wire of cross-sectional area 4×10^−6 m^2 , calculate
the drift velocity of electrons.