Chapter 4
63 Maths Exercise Solutions
A straight wire of mass 
and length 
carries a current of 
. It is suspended in mid-air by a uniform horizontal magnetic field 
What is the magnetic field?
and length carries a current of . It is suspended in mid-air by a uniform horizontal magnetic field What is the magnetic field?If the magnetic field is parallel to the positive 
axis and the charged particle is moving along the positive 
axis 
Fig.
Which way would the Lorentz force be for an electron negative charge
axis and the charged particle is moving along the positive axis Fig. Which way would the Lorentz force be for an electron negative charge If the magnetic field is parallel to the positive 
-axis and the charged particle is moving along the positive 
-axis Fig.
. Which way would the Lorentz force be for a proton positive charge ?
-axis and the charged particle is moving along the positive -axis Fig.. Which way would the Lorentz force be for a proton positive charge ?What is the radius of the path of an electron (mass 
and charge 
) moving at a speed of 
in a magnetic field of 
perpendicular to it? What is its frequency? Calculate its energy in 
. ( 
).
and charge ) moving at a speed of in a magnetic field of perpendicular to it? What is its frequency? Calculate its energy in . ( ).A cyclotron’s oscillator frequency is 
. What should be the operating magnetic field for accelerating protons? If the radius of its ‘dees’ is 
. what is the kinetic energy (in 
) of the proton beam produced by the accelerator.
,
).
. What should be the operating magnetic field for accelerating protons? If the radius of its ‘dees’ is . what is the kinetic energy (in ) of the proton beam produced by the accelerator., ).An element 
is placed at the origin and carries a large current 
. What is the magnetic fleld on the -axis at a distance of 
is placed at the origin and carries a large current . What is the magnetic fleld on the -axis at a distance of A straight wire carrying a current of 
is bent into a semi-circular arc of radius 
as shown in Fig 
. Consider the magnetic field 
at the Centre of the arc.
What is the magnetic field due to the straight segments?
Fig.
is bent into a semi-circular arc of radius as shown in Fig . Consider the magnetic field at the Centre of the arc. What is the magnetic field due to the straight segments?
Fig.
A straight wire carrying a current of is bent into a semi-circular arc of radius 
as shown in Fig.
Consider the magnetic field at the Centre of the arc.
In what way the contribution to from the semicircle differs from that of a circular loop and in what way does it resemble?
is bent into a semi-circular arc of radius as shown in Fig. Consider the magnetic field at the Centre of the arc. In what way the contribution to
from the semicircle differs from that of a circular loop and in what way does it resemble?A straight wire carrying a current of is bent into a semi-circular arc of radius 
as shown in 
Consider the magnetic field at the Centre of the arc. Would your answer be different if the wire were bent into a semi-circular arc of the same radius but in the opposite way as shown in 
?
is bent into a semi-circular arc of radius as shown in Consider the magnetic field at the Centre of the arc. Would your answer be different if the wire were bent into a semi-circular arc of the same radius but in the opposite way as shown in ?Consider a tightly wound 
turn coil of radius 
carrying a current of 
. What is the magnitude of the magnetic field at the centre of the coil?
turn coil of radius carrying a current of . What is the magnitude of the magnetic field at the centre of the coil?Still Have Question?