We need the power law for the change in potential energy (due to the Coulomb force) in bringing a charge q from infinity to distance r from charge Q. We are only interested in the ratio U₁/U₂, so I'm not going to bother with constants (like the permittivity of space).
<span>The potential energy of charge q is proportional to </span>
<span>∫[s=r to ∞] qQs⁻²ds = -qQs⁻¹|[s=r to ∞] = qQr⁻¹, </span>
<span>so if r₂ = 3r₁ and q₂ = q₁/4, then </span>
<span>U₁/U₂ = q₁Qr₂/(r₁q₂Q) = (q₁/q₂)(r₂/r₁) </span>
<span>= 4•3 = 12.</span>
The magnetic force exerted by a field E to a charge q is given by F=Eq. In this case, F=4.30*10^4*(6.80mu C). 1mu C=10^-6C, so F=4.30*6.80=10^-2=0.29N. The direction is in the x direction, the direction that the field is applied because the charge is positive.
Answer:
T = 60 s
Explanation:
There are 6 poles on the track which are equally spaced
so the angular separation between the poles is given as


so the angular speed of the train is given as


now we have time period of the train given as



Answer:
47.76°
Explanation:
Magnitude of dipole moment = 0.0243J/T
Magnetic Field = 57.5mT
kinetic energy = 0.458mJ
∇U = -∇K
Uf - Ui = -0.458mJ
Ui - Uf = 0.458mJ
(-μBcosθi) - (-μBcosθf) = 0.458mJ
rearranging the equation,
(μBcosθf) - (μBcosθi) = 0.458mJ
μB * (cosθf - cosθi) = 0.458mJ
θf is at 0° because the dipole moment is aligned with the magnetic field.
μB * (cos 0 - cos θi) = 0.458mJ
but cos 0 = 1
(0.0243 * 0.0575) (1 - cos θi) = 0.458*10⁻³
1 - cos θi = 0.458*10⁻³ / 1.397*10⁻³
1 - cos θi = 0.3278
collect like terms
cosθi = 0.6722
θ = cos⁻ 0.6722
θ = 47.76°
Answer:
The current is 
Explanation:
From the question we are told that
The radius of the kite string is 
The distance it extended upward is 
The thickness of the water layer is 
The resistivity is 
The potential difference is 
Generally the cross sectional area of the water layer is mathematically represented as

Here r is mathematically represented as
![r = [(R + d ) - R]](https://tex.z-dn.net/?f=r%20%3D%20%20%5B%28R%20%2B%20d%20%29%20-%20R%5D)
=> ![r = [(0.00202 + 0.000506 ) - 0.00202]](https://tex.z-dn.net/?f=r%20%3D%20%20%5B%280.00202%20%2B%20%200.000506%20%29%20-%200.00202%5D)
=> 
=>
=>
Generally the resistance of the water is mathematically represented as

=> 
=> 
Generally the current is mathematically represented as

=> 
=> 