A solenoid of length 75 cm, has a radius of 1 cm and has a total of 750 turns wound on it. It carries a current of 4A. Calculate the magnitude of the axial magnetic field inside the solenoid. If a proton were to move with a speed of 10³ ms^–1 along the axis of this current carrying solenoid, what would be the force experienced by this proton?

Solution

Given, a solenoid.
Length of the solenoid, l = 75 cm
Radius of the coil, r = 1 cm
Number of turns in the coil, N = 750
Current carried by the wire, I = 4 A

Magnetic field inside a solenoid, B = $μ_{o} n I$

Number of turns per metre = $\frac{750}{0.75} = 1000 t u r n s / m$

Therefore,
Magnetic field, B = $4 π \times 10^{- 7} \times 1000 \times 4$ $4 π \times 10^{- 7} \times 1000 \times 4$
= 16 $\times$ 3.14 $\times$ 10^-4
= 5.024 $\times$ 10^-3T

Force experienced by the proton, F
F = qvB sin $θ$
Speed of the proton, v = 10³ m/s
Charge on proton, q = +e = 1.6 $\times 10^{- 19} C$

The direction of magnetic field is along the axis.
$θ$ is the angle between velocity and magnetic field which is 0^oin this case .

$∴ \sin 0 = 0$
Hence the force acting on proton = 0.

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M₁ and M₂ have the following particulars:
R₁ = 10 Ω N₁ = 30,
A₁ = 3.6 x 10^–3 m², B₁ = 0.25 T
R₂ = 14 Ω; N₂ = 42,
A₂ = 1.8 x 10^–3 m², B₂ = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M_1.

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Moving Charges And Magnetism

Some More Questions From Moving Charges And Magnetism Chapter

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