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Two circular loops carry identical currents, but the radius of one loop is twice that of the other.

Valentin [98]

The magnetic field at the center of the 2nd loop is half the magnetic field at the center of the 1st loop.

Explanation:

The magnetic field strength at the center of a current-carrying circular loop is

$B=\frac{\mu_0 I}{2R}$

where

$\mu_0$ is the vacuum permeability

I is the current

R is the radius of the loop

For the first circular loop, we have

$B_1 = \frac{\mu_0 I_1}{2R_1}$

The second loop has

$I_2 = I_1$ (same current)

$R_2 = 2R_1$ (twice the radius)

So, the magnetic field at the centre of the second loop is

$B_2 = \frac{\mu_0 I_2}{2R_2}=\frac{1}{2}(\frac{\mu_0 I_1}{2R_1})=\frac{B_1}{2}$

So, the magnetic field at the center of the 2nd loop is half the magnetic field at the center of the 1st loop.

Learn more about magnetic fields:

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4 0

3 years ago

a proton of mass 1 u travelling with a speed of 3.6 x 10 ^4 m/s has an elastic head on collision with a helium nucleus initially

CaHeK987 [17]

Answer:

Velocity of the helium nuleus = 1.44x10⁴m/s

Velocity of the proton = 2.16x10⁴m/s

Explanation:

From the conservation of linear momentum of the proton collision with the He nucleus:

$P_{1i} + P_{2i} = P_{1f} + P_{2f]$ (1)

where $P_{1i}$ : is the proton linear momentum initial, $P_{2i}$ : is the helium nucleus linear momentum initial, $P_{1f}$ : is the proton linear momentum final, $P_{2f}$ : is the helium nucleus linear momentum final

From (1):

$m_{1}v_{1i} + 0 = m_{1}v_{1f} + m_{2}v_{2f}$ (2)

where m₁ and m₂: are the proton and helium mass, respectively, $v_{1i}$ and $v_{2i}$ : are the proton and helium nucleus velocities, respectively, before the collision, and $v_{1f}$ and $v_{2f}$ : are the proton and helium nucleus velocities, respectively, after the collision

By conservation of energy, we have:

$K_{1i} + K_{2i} = K_{1f} + K_{2f}$ (3)

where $K_{1i}$ and $K_{2i}$ : are the kinetic energy for the proton and helium, respectively, before the colission, and $K_{1f}$ and $K_{2f}$ : are the kinetic energy for the proton and helium, respectively, after the colission