An electron moving with kinetic energyenters a magnetic fieldat right angle to it.The radiusof its circular path will be nearest to a)100cmb)75cmc)25cmd)50cmCorrect answer is option 'D'. Can you explain this answer?

Question

An electron moving with kinetic energyenters a magnetic fieldat right angle to it.The radiusof its circular path will be nearest to  a)100cmb)75cmc)25cmd)50cmCorrect answer is option 'D'. Can you explain this answer?

Answer

Answer

D

Answer

To find the radius of the circular path followed by an electron in a magnetic field, we can use the formula for the centripetal force acting on a charged particle:

F = qvB

where F is the centripetal force, q is the charge of the electron, v is its velocity, and B is the magnetic field strength.

Since the electron is moving in a circular path, the centripetal force can also be expressed as:

F = (mv^2)/r

where m is the mass of the electron and r is the radius of the circular path.

Setting these two expressions for the centripetal force equal to each other, we get:

qvB = (mv^2)/r

Simplifying this equation, we find:

r = (mv)/(qB)

Given:
Kinetic energy of the electron, KE = 6.6 x 10^(-14) J
Magnetic field strength, B = 4 x 10^(-3) T

To find the velocity of the electron, we can use the formula for kinetic energy:

KE = (1/2)mv^2

Solving for v, we get:

v = sqrt((2KE)/m)

Substituting the given values, we find:

v = sqrt((2 * 6.6 x 10^(-14) J)/(9.11 x 10^(-31) kg))
= 1.27 x 10^7 m/s

The charge of an electron is q = -1.6 x 10^(-19) C.

Plugging in these values into the equation for the radius, we get:

r = ((9.11 x 10^(-31) kg) * (1.27 x 10^7 m/s))/(-1.6 x 10^(-19) C * 4 x 10^(-3) T)
= 0.056 m = 5.6 cm

Therefore, the radius of the circular path followed by the electron is closest to 5.6 cm, which is option D.

Answer

Answer

Given data:
Kinetic energy of electron (KE) = 6.6 x 10^-14 J
Magnetic field (B) = 4 x 10^-3 T

To find:
Radius of the circular path (r)

We can use the formula to calculate the radius of the circular path of a charged particle moving in a magnetic field:

r = (mv) / (Be)

where,
m = mass of the electron
v = velocity of the electron
B = magnetic field
e = charge of the electron

Let's calculate each term step by step:

1. Mass of the electron (m):
The mass of an electron is approximately 9.1 x 10^-31 kg.

2. Velocity of the electron (v):
To find the velocity, we need to use the kinetic energy of the electron. The kinetic energy of an object can be calculated using the formula:

KE = (1/2)mv^2

Rearranging the formula, we get:

v = sqrt((2KE) / m)

Substituting the given values, we get:

v = sqrt((2 * 6.6 x 10^-14) / (9.1 x 10^-31))

Calculating the value of v, we find:

v ≈ 1.38 x 10^7 m/s

3. Charge of the electron (e):
The charge of an electron is approximately -1.6 x 10^-19 C.

Now, substituting the values of m, v, B, and e in the formula for the radius of the circular path, we get:

r = [(9.1 x 10^-31) * (1.38 x 10^7)] / [(4 x 10^-3) * (-1.6 x 10^-19)]

Calculating the value of r, we find:

r ≈ 0.127 m

Converting meters to centimeters, we get:

r ≈ 12.7 cm

Therefore, the radius of the circular path of the electron will be nearest to 12.7 cm, which is closest to option D (50 cm).

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