Question

A charge feels a 7.89 x 10-7 N force when it moves 2090 m/s at a 29.4° angle to a 4.23 x 10-3 T magnetic field. What is the amount of the charge?

Answer 1

We have that the amount of the charge q is

$q=1.8*10^{-7}$

From the Question we are told that

Force $F=7.89 x*10^{-7}$

Velocity $V=2090m/s$

Angle $\theta=29.4$

Magnetic field $B=4.23 * 10^{-3} T$

Generally, the equation for Force F is mathematically given by

$F=qVBsin\theta\\\\q=\frac{F}{VBsin\theta}$

$q=\frac{7.89 x*10^{-7}}{4.23 * 10^{-3} T*sin29.4*2090m/s}$

$q=1.8*10^{-7}$

In conclusion

The amount of the charge q is

$q=1.8*10^{-7}$

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Answer 2

From the question, the given charge moving within the magnetic field would have a value of 1.82 x $10^{-7}$ C.

A charge is either a positively or negatively charged particle. When a charge is moving through a magnetic field, it would experience a force which depends on the amount of the charge, its speed, the magnetic field strength and angle. The force on a charge in a magnetic field can be determined by:

F = qvBSin θ

where: q is the charge, v is its velocity/ speed in the field and θ is the angle of deflection of the charge.

Given that: F = 7.89 x $10^{-7}$ N, v = 2090 m/s, B = 4.23 x $10^{-3}$ T and θ = 29.4°.

Thus, the amount of the charge can be determined by;

q = $\frac{F}{vBsin O}$

  = $\frac{7.89*10^{-7} }{2090*4.23*10^{-3}* Sin 29.4 }$

  = $\frac{7.89*10^{-7} }{4.340}$

q = 1.818 x $10^{-7}$

q = 1.82 x $10^{-7}$ C

Therefore, the amount of the charge that moved within the magnetic field is 1.82 x $10^{-7}$ C.

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