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A 10eV electron is circulating in a plane at right angles to a uniform field of magnetic induction 10^-4 Wb/m^2, the orbital radius of electron is A) 11cm B) 18cm C) 12cm D) 16cm?
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**Given Data:**
- Energy of the electron (E) = 10 eV
- Magnetic induction (B) = 10^-4 Wb/m^2

**Formula:**
The formula to calculate the radius of the circular path of a charged particle in a magnetic field is:
r = √(2mE)/(eB²)

where,
- r = radius of the circular path
- m = mass of the electron
- E = energy of the electron
- e = charge of the electron
- B = magnetic induction

**Solution:**
1. Convert the energy of the electron from electron volts (eV) to joules (J):
- 1 eV = 1.602 x 10^-19 J
- E = 10 eV = 10 x 1.602 x 10^-19 J = 1.602 x 10^-18 J

2. Substitute the given values into the formula to calculate the radius:
- m = mass of the electron = 9.1 x 10^-31 kg
- e = charge of the electron = 1.6 x 10^-19 C
- B = 10^-4 Wb/m^2

r = √(2 x 9.1 x 10^-31 kg x 1.602 x 10^-18 J) / (1.6 x 10^-19 C x (10^-4 Wb/m^2)²)

3. Simplify the equation:
- Convert the units of magnetic induction from Wb/m^2 to T (Tesla):
1 Wb/m^2 = 1 T
- B = 10^-4 T

r = √(2 x 9.1 x 10^-31 kg x 1.602 x 10^-18 J) / (1.6 x 10^-19 C x (10^-4 T)²)

r = √(2 x 9.1 x 1.602) / (1.6 x (10^4)²) x 10^-31-18+19

r = √(2 x 9.1 x 1.602) / (1.6 x 10²) x 10^-12

r = √(2 x 9.1 x 1.602) / 1.6 x 10¹⁰

r = (√(2 x 9.1 x 1.602)) / (1.6 x 10¹⁰)

r = (√(2 x 9.1 x 1.602)) / (1.6 x 10¹⁰)

r = (√(29.3544)) / (1.6 x 10¹⁰)

r = 5.423 x 10⁻⁵ m

4. Convert the radius from meters to centimeters:
- 1 m = 100 cm

r = 5.423 x 10⁻⁵ m x 100 cm/m

r = 5.423 x 10⁻³ cm

5. The radius of the circular path of the electron is approximately 5.423 x 10⁻³ cm, which is
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A 10eV electron is circulating in a plane at right angles to a uniform field of magnetic induction 10^-4 Wb/m^2, the orbital radius of electron is A) 11cm B) 18cm C) 12cm D) 16cm?
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