Eletromagnetism (ITA-IME Brazil)

Electricity and Magnetism Level 2

A small sphere with charge q and mass m is released from rest in a uniform electric field (E) in the presence of a uniform magnetic field (B). After a certain time, the sphere describes a trajectory as shown in the image below. Find the value of h. Note: q = 1mC; m = 1g; E = 5N/C; B = 20T

0,015m 0,010m 0,025m 0,020m

Samuel Nascimento by Samuel Nascimento , 24, Brazil

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1 solution

Samuel Nascimento
Jul 16, 2019

qE = qvB-qE

2qE = qvB

v = 2* E B \frac{E}{B}

W = ΔEk

Wfel + Wfmg = m v ² 2 \frac{mv²}{2}

qEh + 0 = m v ² 2 \frac{mv²}{2}

qEh = m 2 \frac{m}{2} * (2* E B \frac{E}{B} )²

h = 2 m E q B ² \frac{2mE}{qB²}

h = 2 ∗ 0.001 k g ∗ 5 ( N / C ) 400 T ² ∗ 0.001 C \frac{2*0.001kg*5(N/C)}{400T²*0.001C}

T = N ∗ s q ∗ m \frac{N*s}{q*m} N = K g ∗ m s ² \frac{Kg*m}{s²}

h = 0.025m

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