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13 Electromagnetism I
Null deflection: If the electric and magnetic fields are crossed, i.e. arranged at
right angles then the charged particle is undeflected. The condition is
v = E/B
(13.5)
Magnetic Induction (B)
B at the Centre of a Coil of N Turns and of Radius r, Carrying Current i
B =
μ 0 Ni
2r
(centre of coil)
(13.6)
The field into the page is indicated by a cross X and out of page by a dot.
B at Distance r from a Long Straight Wire
B =
μ 0 i
2πr
(long wire)
(13.7)
B at Distance r from a Straight Wire of Finite Length
B =
μ 0 i
4πr
(cos θ 1 + cos θ 2 )
(finite wire)
(13.8)
where θ 1 and θ 2 are the inner angles subtended by the field point at the extremities
of the wire.
B on the Axis of a Solenoid
B =
μ 0 Ni
l
(solenoid)
(13.9)
where N is the number of turns over the axial length l.
Magnetic Induction due to a Long Cylindrical Conductor of Radius R
B =
μ 0 ir
2π R 2
(r < R)
=
μ 0 i
2πr
(r > R)
(13.10)
13 Electromagnetism I
Null deflection: If the electric and magnetic fields are crossed, i.e. arranged at
right angles then the charged particle is undeflected. The condition is
v = E/B
(13.5)
Magnetic Induction (B)
B at the Centre of a Coil of N Turns and of Radius r, Carrying Current i
B =
μ 0 Ni
2r
(centre of coil)
(13.6)
The field into the page is indicated by a cross X and out of page by a dot.
B at Distance r from a Long Straight Wire
B =
μ 0 i
2πr
(long wire)
(13.7)
B at Distance r from a Straight Wire of Finite Length
B =
μ 0 i
4πr
(cos θ 1 + cos θ 2 )
(finite wire)
(13.8)
where θ 1 and θ 2 are the inner angles subtended by the field point at the extremities
of the wire.
B on the Axis of a Solenoid
B =
μ 0 Ni
l
(solenoid)
(13.9)
where N is the number of turns over the axial length l.
Magnetic Induction due to a Long Cylindrical Conductor of Radius R
B =
μ 0 ir
2π R 2
(r < R)
=
μ 0 i
2πr
(r > R)
(13.10)